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Flashcard 1428510084364

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#algebra-baldor
Question
Las cantidades conocidas se expresan por [...]
Answer
las primeras letras del alfa beto: a, b, c, d

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Las cantidades conocidas se expresan por las primeras letras del alfa beto: a, b, c, d

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Flashcard 1456761605388

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#48-laws-of-power
Question
Half of the game is learning how to [...] that eat away at you and cloud your reason.
Answer
forget those events in the past

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Half of the game is learning how to forget those events in the past that eat away at you and cloud your reason.

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Flashcard 1480263339276

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#reading-25-understanding-income-statement #revenue-recognition
Question
if Company A sells advertising services (or energy contracts, or commodities) to Company B and almost simultaneously buys an almost identical product from Company B, can Company A report revenue at the fair value of the product sold?

How is this called?
Answer
Round trip transaction

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3.2.3. Barter
and B both report revenue? Such an exchange is referred to as a “barter transaction.” An even more challenging revenue recognition issue evolved from a specific type of barter transaction, a round-trip transaction. As an example, <span>if Company A sells advertising services (or energy contracts, or commodities) to Company B and almost simultaneously buys an almost identical product from Company B, can Company A report revenue at the fair value of the product sold? Because the company’s revenue would be approximately equal to its expense, the net effect of the transaction would have no impact on net income or cash flow. However, the amount of reve







Flashcard 1615974501644

Tags
#cashflow-statement
Question
How does the reporting of investing and financing activities differ in both methods [...] .
Answer
the same for both direct and indirect methods

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Subject 2. Preparing the Cash Flow Statement
are acceptable for financial reporting purposes. However, the direct method discloses more information about a company. Partly because companies want to limit information disclosed, the indirect method is more commonly used. <span>The reporting of investing and financing activities is the same for both direct and indirect methods. Only the reporting of CFO is different. Direct Method Under the direct method, the statement of cash flows reports net cash flows from operations as major clas







#multivariate-normal-distribution
One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution.
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Multivariate normal distribution - Wikipedia
a }}\mathbf {t} {\Big )}} In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. <span>One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly)




#multivariate-normal-distribution
The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value
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Multivariate normal distribution - Wikipedia
e definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. <span>The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value. Contents [hide] 1 Notation and parametrization 2 Definition 3 Properties 3.1 Density function 3.1.1 Non-degenerate case 3.1.2 Degenerate case 3.2 Higher moments 3.3 Lik




#multivariate-normal-distribution
The mutual information of a distribution is a special case of the Kullback–Leibler divergence in which is the full multivariate distribution and is the product of the 1-dimensional marginal distributions
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Multivariate normal distribution - Wikipedia
al {CN}}_{0}\|{\mathcal {CN}}_{1})=\operatorname {tr} \left({\boldsymbol {\Sigma }}_{1}^{-1}{\boldsymbol {\Sigma }}_{0}\right)-k+\ln {|{\boldsymbol {\Sigma }}_{1}| \over |{\boldsymbol {\Sigma }}_{0}|}.} Mutual information[edit source] <span>The mutual information of a distribution is a special case of the Kullback–Leibler divergence in which P {\displaystyle P} is the full multivariate distribution and Q {\displaystyle Q} is the product of the 1-dimensional marginal distributions. In the notation of the Kullback–Leibler divergence section of this article, Σ 1




#multivariate-normal-distribution

In the bivariate case the expression for the mutual information is:

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Multivariate normal distribution - Wikipedia
ldsymbol {\rho }}_{0}} is the correlation matrix constructed from Σ 0 {\displaystyle {\boldsymbol {\Sigma }}_{0}} . <span>In the bivariate case the expression for the mutual information is: I ( x ; y ) = − 1 2 ln ⁡ ( 1 − ρ 2 ) . {\displaystyle I(x;y)=-{1 \over 2}\ln(1-\rho ^{2}).} Cumulative distribution function[edit source] The notion of cumulative distribution function (cdf) in dimension 1 can be extended in two ways to the multidimensional case, based




#multivariate-normal-distribution
Conditional distributions

If N-dimensional x is partitioned as follows

and accordingly μ and Σ are partitioned as follows


then the distribution of x1 conditional on x2 = a is multivariate normal (x1 | x2 = a) ~ N( μ , Σ ) where

and covariance matrix


This matrix is the Schur complement of Σ22 in Σ. This means that to calculate the conditional covariance matrix, one inverts the overall covariance matrix, drops the rows and columns corresponding to the variables being conditioned upon, and then inverts back to get the conditional covariance matrix. Here is the generalized inverse of .

Note that knowing that x2 = a alters the variance, though the new variance does not depend on the specific value of a; perhaps more surprisingly, the mean is shifted by ; compare this with the situation of not knowing the value of a, in which case x1 would have distribution .

An interesting fact derived in order to prove this result, is that the random vectors and are independent.

The matrix Σ12Σ22−1 is known as the matrix of regression co

...
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Multivariate normal distribution - Wikipedia
y two or more of its components that are pairwise independent are independent. But, as pointed out just above, it is not true that two random variables that are (separately, marginally) normally distributed and uncorrelated are independent. <span>Conditional distributions[edit source] If N-dimensional x is partitioned as follows x = [ x 1 x 2 ] with sizes [ q × 1 ( N − q ) × 1 ] {\displaystyle \mathbf {x} ={\begin{bmatrix}\mathbf {x} _{1}\\\mathbf {x} _{2}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times 1\\(N-q)\times 1\end{bmatrix}}} and accordingly μ and Σ are partitioned as follows μ = [ μ 1 μ 2 ] with sizes [ q × 1 ( N − q ) × 1 ] {\displaystyle {\boldsymbol {\mu }}={\begin{bmatrix}{\boldsymbol {\mu }}_{1}\\{\boldsymbol {\mu }}_{2}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times 1\\(N-q)\times 1\end{bmatrix}}} Σ = [ Σ 11 Σ 12 Σ 21 Σ 22 ] with sizes [ q × q q × ( N − q ) ( N − q ) × q ( N − q ) × ( N − q ) ] {\displaystyle {\boldsymbol {\Sigma }}={\begin{bmatrix}{\boldsymbol {\Sigma }}_{11}&{\boldsymbol {\Sigma }}_{12}\\{\boldsymbol {\Sigma }}_{21}&{\boldsymbol {\Sigma }}_{22}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times q&q\times (N-q)\\(N-q)\times q&(N-q)\times (N-q)\end{bmatrix}}} then the distribution of x 1 conditional on x 2 = a is multivariate normal (x 1 | x 2 = a) ~ N(μ, Σ) where μ ¯ = μ 1 + Σ 12 Σ 22 − 1 ( a − μ 2 ) {\displaystyle {\bar {\boldsymbol {\mu }}}={\boldsymbol {\mu }}_{1}+{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\left(\mathbf {a} -{\boldsymbol {\mu }}_{2}\right)} and covariance matrix Σ ¯ = Σ 11 − Σ 12 Σ 22 − 1 Σ 21 . {\displaystyle {\overline {\boldsymbol {\Sigma }}}={\boldsymbol {\Sigma }}_{11}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}{\boldsymbol {\Sigma }}_{21}.} [13] This matrix is the Schur complement of Σ 22 in Σ. This means that to calculate the conditional covariance matrix, one inverts the overall covariance matrix, drops the rows and columns corresponding to the variables being conditioned upon, and then inverts back to get the conditional covariance matrix. Here Σ 22 − 1 {\displaystyle {\boldsymbol {\Sigma }}_{22}^{-1}} is the generalized inverse of Σ 22 {\displaystyle {\boldsymbol {\Sigma }}_{22}} . Note that knowing that x 2 = a alters the variance, though the new variance does not depend on the specific value of a; perhaps more surprisingly, the mean is shifted by Σ 12 Σ 22 − 1 ( a − μ 2 ) {\displaystyle {\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\left(\mathbf {a} -{\boldsymbol {\mu }}_{2}\right)} ; compare this with the situation of not knowing the value of a, in which case x 1 would have distribution N q ( μ 1 , Σ 11 ) {\displaystyle {\mathcal {N}}_{q}\left({\boldsymbol {\mu }}_{1},{\boldsymbol {\Sigma }}_{11}\right)} . An interesting fact derived in order to prove this result, is that the random vectors x 2 {\displaystyle \mathbf {x} _{2}} and y 1 = x 1 − Σ 12 Σ 22 − 1 x 2 {\displaystyle \mathbf {y} _{1}=\mathbf {x} _{1}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\mathbf {x} _{2}} are independent. The matrix Σ 12 Σ 22 −1 is known as the matrix of regression coefficients. Bivariate case[edit source] In the bivariate case where x is partitioned into X 1 and X 2 , the conditional distribution of X 1 given X 2 is [14]




#multivariate-normal-distribution

To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra.[16]

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Multivariate normal distribution - Wikipedia
) {\displaystyle \operatorname {E} (X_{1}\mid X_{2}##BAD TAG##\rho E(X_{2}\mid X_{2}##BAD TAG##} and then using the properties of the expectation of a truncated normal distribution. Marginal distributions[edit source] <span>To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra. [16] Example Let X = [X 1 , X 2 , X 3 ] be multivariate normal random variables with mean vector μ = [μ 1 , μ 2 , μ 3 ] and covariance matrix Σ (standard parametrization for multivariate




#multivariate-normal-distribution
If Y = c + BX is an affine transformation of where c is an vector of constants and B is a constant matrix, then Y has a multivariate normal distribution with expected value c + and variance BΣBT .

Corollaries: sums of Gaussian are Gaussian, marginals of Gaussian are Gaussian.
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Multivariate normal distribution - Wikipedia
{\displaystyle {\boldsymbol {\Sigma }}'={\begin{bmatrix}{\boldsymbol {\Sigma }}_{11}&{\boldsymbol {\Sigma }}_{13}\\{\boldsymbol {\Sigma }}_{31}&{\boldsymbol {\Sigma }}_{33}\end{bmatrix}}} . Affine transformation[edit source] <span>If Y = c + BX is an affine transformation of X ∼ N ( μ , Σ ) , {\displaystyle \mathbf {X} \ \sim {\mathcal {N}}({\boldsymbol {\mu }},{\boldsymbol {\Sigma }}),} where c is an M × 1 {\displaystyle M\times 1} vector of constants and B is a constant M × N {\displaystyle M\times N} matrix, then Y has a multivariate normal distribution with expected value c + Bμ and variance BΣB T i.e., Y ∼ N ( c + B μ , B Σ B T ) {\displaystyle \mathbf {Y} \sim {\mathcal {N}}\left(\mathbf {c} +\mathbf {B} {\boldsymbol {\mu }},\mathbf {B} {\boldsymbol {\Sigma }}\mathbf {B} ^{\rm {T}}\right)} . In particular, any subset of the X i has a marginal distribution that is also multivariate normal. To see this, consider the following example: to extract the subset (X 1 , X 2 , X 4 )




#multivariate-normal-distribution
The equidensity contours of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean.
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Multivariate normal distribution - Wikipedia
implies that the variance of the dot product must be positive. An affine transformation of X such as 2X is not the same as the sum of two independent realisations of X. Geometric interpretation[edit source] See also: Confidence region <span>The equidensity contours of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean. [17] Hence the multivariate normal distribution is an example of the class of elliptical distributions. The directions of the principal axes of the ellipsoids are given by the eigenvec




#multivariate-normal-distribution
The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix Σ. The squared relative lengths of the principal axes are given by the corresponding eigenvalues.
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Multivariate normal distribution - Wikipedia
urs of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean. [17] Hence the multivariate normal distribution is an example of the class of elliptical distributions. <span>The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix Σ. The squared relative lengths of the principal axes are given by the corresponding eigenvalues. If Σ = UΛU T = UΛ 1/2 (UΛ 1/2 ) T is an eigendecomposition where the columns of U are unit eigenvectors and Λ is a diagonal matrix of the eigenvalues, then we have




#multivariate-normal-distribution
The distribution N(μ, Σ) is in effect N(0, I) scaled by Λ1/2, rotated by U and translated by μ.
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Multivariate normal distribution - Wikipedia
{\mu }}+\mathbf {U} {\mathcal {N}}(0,{\boldsymbol {\Lambda }}).} Moreover, U can be chosen to be a rotation matrix, as inverting an axis does not have any effect on N(0, Λ), but inverting a column changes the sign of U's determinant. <span>The distribution N(μ, Σ) is in effect N(0, I) scaled by Λ 1/2 , rotated by U and translated by μ. Conversely, any choice of μ, full rank matrix U, and positive diagonal entries Λ i yields a non-singular multivariate normal distribution. If any Λ i is zero and U is square, the re




#multivariate-normal-distribution

In the bivariate case where x is partitioned into X1 and X2, the conditional distribution of X1 given X2 is

where is the correlation coefficient between X1 and X2.

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Multivariate normal distribution - Wikipedia
mathbf {y} _{1}=\mathbf {x} _{1}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\mathbf {x} _{2}} are independent. The matrix Σ 12 Σ 22 −1 is known as the matrix of regression coefficients. Bivariate case[edit source] <span>In the bivariate case where x is partitioned into X 1 and X 2 , the conditional distribution of X 1 given X 2 is [14] X 1 ∣ X 2 = x 2 ∼ N ( μ 1 + σ 1 σ 2 ρ ( x 2 − μ 2 ) , ( 1 − ρ 2 ) σ 1 2 ) . {\displaystyle X_{1}\mid X_{2}=x_{2}\ \sim \ {\mathcal {N}}\left(\mu _{1}+{\frac {\sigma _{1}}{\sigma _{2}}}\rho (x_{2}-\mu _{2}),\,(1-\rho ^{2})\sigma _{1}^{2}\right).} where ρ {\displaystyle \rho } is the correlation coefficient between X 1 and X 2 . Bivariate conditional expectation[edit source] In the general case[edit source] (




Flashcard 1729607109900

Tags
#multivariate-normal-distribution
Question

In the bivariate case, the conditional mean of X1 given X2 is [...]

Answer
\( \mu_1 + \frac{\sigma_1}{\sigma_2} \rho (x_2 - \mu_2) \)

where is the correlation coefficient between X1 and X2.
Apparently both the correlation and variance should play a part!

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In the bivariate case where x is partitioned into X 1 and X 2 , the conditional distribution of X 1 given X 2 is where is the correlation coefficient between X 1 and X 2 .

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Multivariate normal distribution - Wikipedia
mathbf {y} _{1}=\mathbf {x} _{1}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\mathbf {x} _{2}} are independent. The matrix Σ 12 Σ 22 −1 is known as the matrix of regression coefficients. Bivariate case[edit source] <span>In the bivariate case where x is partitioned into X 1 and X 2 , the conditional distribution of X 1 given X 2 is [14] X 1 ∣ X 2 = x 2 ∼ N ( μ 1 + σ 1 σ 2 ρ ( x 2 − μ 2 ) , ( 1 − ρ 2 ) σ 1 2 ) . {\displaystyle X_{1}\mid X_{2}=x_{2}\ \sim \ {\mathcal {N}}\left(\mu _{1}+{\frac {\sigma _{1}}{\sigma _{2}}}\rho (x_{2}-\mu _{2}),\,(1-\rho ^{2})\sigma _{1}^{2}\right).} where ρ {\displaystyle \rho } is the correlation coefficient between X 1 and X 2 . Bivariate conditional expectation[edit source] In the general case[edit source] (







Flashcard 1729664257292

Tags
#multivariate-normal-distribution
Question
The distribution N(μ, Σ) is in effect N(0, I) scaled by [...] , rotated by [...] and translated by [...] .
Answer
Λ1/2, U , μ.

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The distribution N(μ, Σ) is in effect N(0, I) scaled by Λ 1/2 , rotated by U and translated by μ.

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Multivariate normal distribution - Wikipedia
{\mu }}+\mathbf {U} {\mathcal {N}}(0,{\boldsymbol {\Lambda }}).} Moreover, U can be chosen to be a rotation matrix, as inverting an axis does not have any effect on N(0, Λ), but inverting a column changes the sign of U's determinant. <span>The distribution N(μ, Σ) is in effect N(0, I) scaled by Λ 1/2 , rotated by U and translated by μ. Conversely, any choice of μ, full rank matrix U, and positive diagonal entries Λ i yields a non-singular multivariate normal distribution. If any Λ i is zero and U is square, the re







Flashcard 1729666616588

Tags
#multivariate-normal-distribution
Question
The directions of the principal axes of the ellipsoids are given by [...] of the covariance matrix Σ
Answer
the eigenvectors

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The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix Σ. The squared relative lengths of the principal axes are given by the corresponding eigenvalues.

Original toplevel document

Multivariate normal distribution - Wikipedia
urs of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean. [17] Hence the multivariate normal distribution is an example of the class of elliptical distributions. <span>The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix Σ. The squared relative lengths of the principal axes are given by the corresponding eigenvalues. If Σ = UΛU T = UΛ 1/2 (UΛ 1/2 ) T is an eigendecomposition where the columns of U are unit eigenvectors and Λ is a diagonal matrix of the eigenvalues, then we have







Flashcard 1729668189452

Tags
#multivariate-normal-distribution
Question
[...] of the principal axes are given by the corresponding eigenvalues.
Answer
The squared relative lengths

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The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix Σ. The squared relative lengths of the principal axes are given by the corresponding eigenvalues.

Original toplevel document

Multivariate normal distribution - Wikipedia
urs of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean. [17] Hence the multivariate normal distribution is an example of the class of elliptical distributions. <span>The directions of the principal axes of the ellipsoids are given by the eigenvectors of the covariance matrix Σ. The squared relative lengths of the principal axes are given by the corresponding eigenvalues. If Σ = UΛU T = UΛ 1/2 (UΛ 1/2 ) T is an eigendecomposition where the columns of U are unit eigenvectors and Λ is a diagonal matrix of the eigenvalues, then we have







Flashcard 1729669762316

Tags
#multivariate-normal-distribution
Question
The equidensity contours of a non-singular multivariate normal distribution are [...] centered at the mean.
Answer
ellipsoids

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The equidensity contours of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean.

Original toplevel document

Multivariate normal distribution - Wikipedia
implies that the variance of the dot product must be positive. An affine transformation of X such as 2X is not the same as the sum of two independent realisations of X. Geometric interpretation[edit source] See also: Confidence region <span>The equidensity contours of a non-singular multivariate normal distribution are ellipsoids (i.e. linear transformations of hyperspheres) centered at the mean. [17] Hence the multivariate normal distribution is an example of the class of elliptical distributions. The directions of the principal axes of the ellipsoids are given by the eigenvec







Flashcard 1729672908044

Tags
#multivariate-normal-distribution
Question
If Y = c + BX is an affine transformation,
then Y has a multivariate normal distribution with expected value [...]
Answer
c +

Corollaries: sums of Gaussian are Gaussian, marginals of Gaussian are Gaussian.

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If Y = c + BX is an affine transformation of where c is an vector of constants and B is a constant matrix, then Y has a multivariate normal distribution with expected value c + Bμ and variance BΣB T . Corollaries: sums of Gaussian are Gaussian, marginals of Gaussian are Gaussian.

Original toplevel document

Multivariate normal distribution - Wikipedia
{\displaystyle {\boldsymbol {\Sigma }}'={\begin{bmatrix}{\boldsymbol {\Sigma }}_{11}&{\boldsymbol {\Sigma }}_{13}\\{\boldsymbol {\Sigma }}_{31}&{\boldsymbol {\Sigma }}_{33}\end{bmatrix}}} . Affine transformation[edit source] <span>If Y = c + BX is an affine transformation of X ∼ N ( μ , Σ ) , {\displaystyle \mathbf {X} \ \sim {\mathcal {N}}({\boldsymbol {\mu }},{\boldsymbol {\Sigma }}),} where c is an M × 1 {\displaystyle M\times 1} vector of constants and B is a constant M × N {\displaystyle M\times N} matrix, then Y has a multivariate normal distribution with expected value c + Bμ and variance BΣB T i.e., Y ∼ N ( c + B μ , B Σ B T ) {\displaystyle \mathbf {Y} \sim {\mathcal {N}}\left(\mathbf {c} +\mathbf {B} {\boldsymbol {\mu }},\mathbf {B} {\boldsymbol {\Sigma }}\mathbf {B} ^{\rm {T}}\right)} . In particular, any subset of the X i has a marginal distribution that is also multivariate normal. To see this, consider the following example: to extract the subset (X 1 , X 2 , X 4 )







Flashcard 1729674480908

Tags
#multivariate-normal-distribution
Question
If Y = c + BX, then Y has variance [...]
Answer
BΣBT

Corollaries: sums of Gaussian are Gaussian, marginals of Gaussian are Gaussian.

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><head> If Y = c + BX is an affine transformation of where c is an vector of constants and B is a constant matrix, then Y has a multivariate normal distribution with expected value c + Bμ and variance BΣB T . Corollaries: sums of Gaussian are Gaussian, marginals of Gaussian are Gaussian. <html>

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Multivariate normal distribution - Wikipedia
{\displaystyle {\boldsymbol {\Sigma }}'={\begin{bmatrix}{\boldsymbol {\Sigma }}_{11}&{\boldsymbol {\Sigma }}_{13}\\{\boldsymbol {\Sigma }}_{31}&{\boldsymbol {\Sigma }}_{33}\end{bmatrix}}} . Affine transformation[edit source] <span>If Y = c + BX is an affine transformation of X ∼ N ( μ , Σ ) , {\displaystyle \mathbf {X} \ \sim {\mathcal {N}}({\boldsymbol {\mu }},{\boldsymbol {\Sigma }}),} where c is an M × 1 {\displaystyle M\times 1} vector of constants and B is a constant M × N {\displaystyle M\times N} matrix, then Y has a multivariate normal distribution with expected value c + Bμ and variance BΣB T i.e., Y ∼ N ( c + B μ , B Σ B T ) {\displaystyle \mathbf {Y} \sim {\mathcal {N}}\left(\mathbf {c} +\mathbf {B} {\boldsymbol {\mu }},\mathbf {B} {\boldsymbol {\Sigma }}\mathbf {B} ^{\rm {T}}\right)} . In particular, any subset of the X i has a marginal distribution that is also multivariate normal. To see this, consider the following example: to extract the subset (X 1 , X 2 , X 4 )







Flashcard 1729676053772

Tags
#multivariate-normal-distribution
Question

To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to [...]

Answer
drop the irrelevant variables

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To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions an

Original toplevel document

Multivariate normal distribution - Wikipedia
) {\displaystyle \operatorname {E} (X_{1}\mid X_{2}##BAD TAG##\rho E(X_{2}\mid X_{2}##BAD TAG##} and then using the properties of the expectation of a truncated normal distribution. Marginal distributions[edit source] <span>To obtain the marginal distribution over a subset of multivariate normal random variables, one only needs to drop the irrelevant variables (the variables that one wants to marginalize out) from the mean vector and the covariance matrix. The proof for this follows from the definitions of multivariate normal distributions and linear algebra. [16] Example Let X = [X 1 , X 2 , X 3 ] be multivariate normal random variables with mean vector μ = [μ 1 , μ 2 , μ 3 ] and covariance matrix Σ (standard parametrization for multivariate







#multivariate-normal-distribution

the distribution of x1 conditional on x2 = a is multivariate normal (x1 | x2 = a) ~ N( μ , Σ ) where and covariance matrix

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Conditional distributions If N-dimensional x is partitioned as follows and accordingly μ and Σ are partitioned as follows then the distribution of x 1 conditional on x 2 = a is multivariate normal (x 1 | x 2 = a) ~ N( μ , Σ ) where and covariance matrix This matrix is the Schur complement of Σ 22 in Σ. This means that to calculate the conditional covariance matrix, one inverts the overall covariance matrix, drops t

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Multivariate normal distribution - Wikipedia
y two or more of its components that are pairwise independent are independent. But, as pointed out just above, it is not true that two random variables that are (separately, marginally) normally distributed and uncorrelated are independent. <span>Conditional distributions[edit source] If N-dimensional x is partitioned as follows x = [ x 1 x 2 ] with sizes [ q × 1 ( N − q ) × 1 ] {\displaystyle \mathbf {x} ={\begin{bmatrix}\mathbf {x} _{1}\\\mathbf {x} _{2}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times 1\\(N-q)\times 1\end{bmatrix}}} and accordingly μ and Σ are partitioned as follows μ = [ μ 1 μ 2 ] with sizes [ q × 1 ( N − q ) × 1 ] {\displaystyle {\boldsymbol {\mu }}={\begin{bmatrix}{\boldsymbol {\mu }}_{1}\\{\boldsymbol {\mu }}_{2}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times 1\\(N-q)\times 1\end{bmatrix}}} Σ = [ Σ 11 Σ 12 Σ 21 Σ 22 ] with sizes [ q × q q × ( N − q ) ( N − q ) × q ( N − q ) × ( N − q ) ] {\displaystyle {\boldsymbol {\Sigma }}={\begin{bmatrix}{\boldsymbol {\Sigma }}_{11}&{\boldsymbol {\Sigma }}_{12}\\{\boldsymbol {\Sigma }}_{21}&{\boldsymbol {\Sigma }}_{22}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times q&q\times (N-q)\\(N-q)\times q&(N-q)\times (N-q)\end{bmatrix}}} then the distribution of x 1 conditional on x 2 = a is multivariate normal (x 1 | x 2 = a) ~ N(μ, Σ) where μ ¯ = μ 1 + Σ 12 Σ 22 − 1 ( a − μ 2 ) {\displaystyle {\bar {\boldsymbol {\mu }}}={\boldsymbol {\mu }}_{1}+{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\left(\mathbf {a} -{\boldsymbol {\mu }}_{2}\right)} and covariance matrix Σ ¯ = Σ 11 − Σ 12 Σ 22 − 1 Σ 21 . {\displaystyle {\overline {\boldsymbol {\Sigma }}}={\boldsymbol {\Sigma }}_{11}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}{\boldsymbol {\Sigma }}_{21}.} [13] This matrix is the Schur complement of Σ 22 in Σ. This means that to calculate the conditional covariance matrix, one inverts the overall covariance matrix, drops the rows and columns corresponding to the variables being conditioned upon, and then inverts back to get the conditional covariance matrix. Here Σ 22 − 1 {\displaystyle {\boldsymbol {\Sigma }}_{22}^{-1}} is the generalized inverse of Σ 22 {\displaystyle {\boldsymbol {\Sigma }}_{22}} . Note that knowing that x 2 = a alters the variance, though the new variance does not depend on the specific value of a; perhaps more surprisingly, the mean is shifted by Σ 12 Σ 22 − 1 ( a − μ 2 ) {\displaystyle {\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\left(\mathbf {a} -{\boldsymbol {\mu }}_{2}\right)} ; compare this with the situation of not knowing the value of a, in which case x 1 would have distribution N q ( μ 1 , Σ 11 ) {\displaystyle {\mathcal {N}}_{q}\left({\boldsymbol {\mu }}_{1},{\boldsymbol {\Sigma }}_{11}\right)} . An interesting fact derived in order to prove this result, is that the random vectors x 2 {\displaystyle \mathbf {x} _{2}} and y 1 = x 1 − Σ 12 Σ 22 − 1 x 2 {\displaystyle \mathbf {y} _{1}=\mathbf {x} _{1}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\mathbf {x} _{2}} are independent. The matrix Σ 12 Σ 22 −1 is known as the matrix of regression coefficients. Bivariate case[edit source] In the bivariate case where x is partitioned into X 1 and X 2 , the conditional distribution of X 1 given X 2 is [14]




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the distribution of x1 conditional on x2 = a is multivariate normal (x1 | x2 = a) ~ N( μ , Σ ) where μ [...] and covariance matrix Σ [...]

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the distribution of x 1 conditional on x 2 = a is multivariate normal (x 1 | x 2 = a) ~ N( μ , Σ ) where and covariance matrix

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Multivariate normal distribution - Wikipedia
y two or more of its components that are pairwise independent are independent. But, as pointed out just above, it is not true that two random variables that are (separately, marginally) normally distributed and uncorrelated are independent. <span>Conditional distributions[edit source] If N-dimensional x is partitioned as follows x = [ x 1 x 2 ] with sizes [ q × 1 ( N − q ) × 1 ] {\displaystyle \mathbf {x} ={\begin{bmatrix}\mathbf {x} _{1}\\\mathbf {x} _{2}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times 1\\(N-q)\times 1\end{bmatrix}}} and accordingly μ and Σ are partitioned as follows μ = [ μ 1 μ 2 ] with sizes [ q × 1 ( N − q ) × 1 ] {\displaystyle {\boldsymbol {\mu }}={\begin{bmatrix}{\boldsymbol {\mu }}_{1}\\{\boldsymbol {\mu }}_{2}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times 1\\(N-q)\times 1\end{bmatrix}}} Σ = [ Σ 11 Σ 12 Σ 21 Σ 22 ] with sizes [ q × q q × ( N − q ) ( N − q ) × q ( N − q ) × ( N − q ) ] {\displaystyle {\boldsymbol {\Sigma }}={\begin{bmatrix}{\boldsymbol {\Sigma }}_{11}&{\boldsymbol {\Sigma }}_{12}\\{\boldsymbol {\Sigma }}_{21}&{\boldsymbol {\Sigma }}_{22}\end{bmatrix}}{\text{ with sizes }}{\begin{bmatrix}q\times q&q\times (N-q)\\(N-q)\times q&(N-q)\times (N-q)\end{bmatrix}}} then the distribution of x 1 conditional on x 2 = a is multivariate normal (x 1 | x 2 = a) ~ N(μ, Σ) where μ ¯ = μ 1 + Σ 12 Σ 22 − 1 ( a − μ 2 ) {\displaystyle {\bar {\boldsymbol {\mu }}}={\boldsymbol {\mu }}_{1}+{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\left(\mathbf {a} -{\boldsymbol {\mu }}_{2}\right)} and covariance matrix Σ ¯ = Σ 11 − Σ 12 Σ 22 − 1 Σ 21 . {\displaystyle {\overline {\boldsymbol {\Sigma }}}={\boldsymbol {\Sigma }}_{11}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}{\boldsymbol {\Sigma }}_{21}.} [13] This matrix is the Schur complement of Σ 22 in Σ. This means that to calculate the conditional covariance matrix, one inverts the overall covariance matrix, drops the rows and columns corresponding to the variables being conditioned upon, and then inverts back to get the conditional covariance matrix. Here Σ 22 − 1 {\displaystyle {\boldsymbol {\Sigma }}_{22}^{-1}} is the generalized inverse of Σ 22 {\displaystyle {\boldsymbol {\Sigma }}_{22}} . Note that knowing that x 2 = a alters the variance, though the new variance does not depend on the specific value of a; perhaps more surprisingly, the mean is shifted by Σ 12 Σ 22 − 1 ( a − μ 2 ) {\displaystyle {\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\left(\mathbf {a} -{\boldsymbol {\mu }}_{2}\right)} ; compare this with the situation of not knowing the value of a, in which case x 1 would have distribution N q ( μ 1 , Σ 11 ) {\displaystyle {\mathcal {N}}_{q}\left({\boldsymbol {\mu }}_{1},{\boldsymbol {\Sigma }}_{11}\right)} . An interesting fact derived in order to prove this result, is that the random vectors x 2 {\displaystyle \mathbf {x} _{2}} and y 1 = x 1 − Σ 12 Σ 22 − 1 x 2 {\displaystyle \mathbf {y} _{1}=\mathbf {x} _{1}-{\boldsymbol {\Sigma }}_{12}{\boldsymbol {\Sigma }}_{22}^{-1}\mathbf {x} _{2}} are independent. The matrix Σ 12 Σ 22 −1 is known as the matrix of regression coefficients. Bivariate case[edit source] In the bivariate case where x is partitioned into X 1 and X 2 , the conditional distribution of X 1 given X 2 is [14]







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In the bivariate normal case the expression for the mutual information is [...]

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In the bivariate case the expression for the mutual information is:

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Multivariate normal distribution - Wikipedia
ldsymbol {\rho }}_{0}} is the correlation matrix constructed from Σ 0 {\displaystyle {\boldsymbol {\Sigma }}_{0}} . <span>In the bivariate case the expression for the mutual information is: I ( x ; y ) = − 1 2 ln ⁡ ( 1 − ρ 2 ) . {\displaystyle I(x;y)=-{1 \over 2}\ln(1-\rho ^{2}).} Cumulative distribution function[edit source] The notion of cumulative distribution function (cdf) in dimension 1 can be extended in two ways to the multidimensional case, based







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The mutual information of a distribution is a special case of the Kullback–Leibler divergence in which is [...] and is [...]
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the full multivariate distribution, the product of the 1-dimensional marginal distributions

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The mutual information of a distribution is a special case of the Kullback–Leibler divergence in which is the full multivariate distribution and is the product of the 1-dimensional marginal distributions

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Multivariate normal distribution - Wikipedia
al {CN}}_{0}\|{\mathcal {CN}}_{1})=\operatorname {tr} \left({\boldsymbol {\Sigma }}_{1}^{-1}{\boldsymbol {\Sigma }}_{0}\right)-k+\ln {|{\boldsymbol {\Sigma }}_{1}| \over |{\boldsymbol {\Sigma }}_{0}|}.} Mutual information[edit source] <span>The mutual information of a distribution is a special case of the Kullback–Leibler divergence in which P {\displaystyle P} is the full multivariate distribution and Q {\displaystyle Q} is the product of the 1-dimensional marginal distributions. In the notation of the Kullback–Leibler divergence section of this article, Σ 1







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The multivariate normal distribution is often used to describe correlated real-valued random variables each of which [...]
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clusters around a mean value

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The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value

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Multivariate normal distribution - Wikipedia
e definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. <span>The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value. Contents [hide] 1 Notation and parametrization 2 Definition 3 Properties 3.1 Density function 3.1.1 Non-degenerate case 3.1.2 Degenerate case 3.2 Higher moments 3.3 Lik







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a random vector is said to be k-variate normally distributed if [...] has a univariate normal distribution.
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every linear combination of its k components

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One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution.

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Multivariate normal distribution - Wikipedia
a }}\mathbf {t} {\Big )}} In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. <span>One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly)







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If the covariance matrix is not full rank, then the multivariate normal distribution is degenerate and does not have a density.
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Multivariate normal distribution - Wikipedia
operatorname {sgn}(\rho ){\frac {\sigma _{Y}}{\sigma _{X}}}(x-\mu _{X})+\mu _{Y}.} This is because this expression, with sgn(ρ) replaced by ρ, is the best linear unbiased prediction of Y given a value of X. [4] Degenerate case[edit] <span>If the covariance matrix Σ {\displaystyle {\boldsymbol {\Sigma }}} is not full rank, then the multivariate normal distribution is degenerate and does not have a density. More precisely, it does not have a density with respect to k-dimensional Lebesgue measure (which is the usual measure assumed in calculus-level probability courses). Only random vectors




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If [...], then the multivariate normal distribution is degenerate and does not have a density.
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the covariance matrix is not full rank

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If the covariance matrix is not full rank, then the multivariate normal distribution is degenerate and does not have a density.

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Multivariate normal distribution - Wikipedia
operatorname {sgn}(\rho ){\frac {\sigma _{Y}}{\sigma _{X}}}(x-\mu _{X})+\mu _{Y}.} This is because this expression, with sgn(ρ) replaced by ρ, is the best linear unbiased prediction of Y given a value of X. [4] Degenerate case[edit] <span>If the covariance matrix Σ {\displaystyle {\boldsymbol {\Sigma }}} is not full rank, then the multivariate normal distribution is degenerate and does not have a density. More precisely, it does not have a density with respect to k-dimensional Lebesgue measure (which is the usual measure assumed in calculus-level probability courses). Only random vectors







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A staggered board consists of a board of directors whose members are [...]
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grouped into classes; for example, Class 1, Class 2, Class 3, etc.

Each class represents a certain percentage of the total number of board positions.

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A staggered board consists of a board of directors whose members are grouped into classes; for example, Class 1, Class 2, Class 3, etc. Each class represents a certain percentage of the total number of board positions.

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Staggered Board
[imagelink] DEFINITION of '<span>Staggered Board' A staggered board consists of a board of directors whose members are grouped into classes; for example, Class 1, Class 2, Class 3, etc. Each class represents a certain percentage of the total number of board positions. For example, a class is commonly comprised on one-third of the total board members. During each election term only one class is open to elections, thereby staggering the board directorship. BREAKING DOWN 'Staggered Board' A staggered board is also known as a classified board because of the different "classes" involved. A







I don’t consider myself in the real estate business! I’m in the marketing business.
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You will find good deals through effective marketing. You’ll find lenders willing to do no-money-down deals through marketing. And you will employ other marketing techniques to sell your deals at a handsome profit to other people.
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It doesn’t matter how much skill you have; it doesn’t matter how much knowledge you’ve accumulated: If your phone is not ringing and the mailbox is empty, you’re not going anywhere
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Have a whole bunch of marketing tools to apply to any market at any time.
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Create a pipeline of deals presenting themselves through the phone, e-mail, and post office. Once you’ve turned on that pipeline, never turn it off ! It’s your goose that’s laying your golden deals. Deal flow is the engine that drives your business.
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Analyze the Deals Once you start getting leads coming in to your business from all of your marketing, it’s time to separate the good deals from the bad. The majority of what you’ll see in the beginning will be worthless deals. No big deal. It’s just the nature of the beast.
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build a start-to-finish, successful real estate farming strategy using RPR’s dynamic data and impressive reports, available only to REALTORS ® .
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Farming, also known as geographical prospecting, is a proven method of marketing your real estate business to a neighborhood or local proximity in a way that raises awareness of your brand, captures leads, earns referrals, and gains listings.
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Property Resource ® (RPR ® ) will provide all of the data and reports you need to execute a profit-yielding endeavor.
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A predetermined set of criteria for establishing your farm area will help save time and energy
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Operating a farm area outside your normal commute can be a challenge if you want the campaign to be consistent and affordable. A consistent effort includes touch points at least every three to four weeks, on a long term basis, so easy access to your farm area is an important consideration.
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know how to calculate turnover
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Divide the number of sales in the last 12 months by the number of homes in the area. For example: From your geographic area, 15 houses have been sold in the past 12 months. There are 150 homes in the area. (15 ÷ 150) x 100 = 10% turnover rate. You typically want to see 5-7% turnover rate or higher.
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Look to RPR heat maps to determine whether values in your farm area are increasing or decreasing over time.
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find the 12-month change in estimated values, list vs sales prices, and the density of distressed properties
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Static random-access memory (static RAM or SRAM) is a type of semiconductor memory that uses bistable latching circuitry (flip-flop) to store each bit.
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Historical Paper data storage (1725) Drum memory (1932) Magnetic-core memory (1949) Plated wire memory (1957) Core rope memory (1960s) Thin-film memory (1962) Twistor memory (~1968) Bubble memory (~1970) Floppy disk (1971) v t e <span>Static random-access memory (static RAM or SRAM) is a type of semiconductor memory that uses bistable latching circuitry (flip-flop) to store each bit. SRAM exhibits data remanence, [1] but it is still volatile in the conventional sense that data is eventually lost when the memory is not powered. The term static differentiates SRAM




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The power consumption of SRAM varies widely depending on how frequently it is accessed; in some instances, it can use as much power as dynamic RAM, when used at high frequencies, and some ICs can consume many watts at full bandwidth. On the other hand, static RAM used at a somewhat slower pace, such as in applications with moderately clocked microprocessors, draws very little power and can have a nearly negligible power consumption when sitting idle – in the region of a few micro-watts. Several techniques have been proposed to manage power consumption of SRAM-based memory structures.[2]


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Static random-access memory - Wikipedia
VGT6 microcontroller as seen by an optical microscope. Characteristics[edit] Advantages: Low power consumption Simplicity – a refresh circuit is not needed Reliability Disadvantages: Price Capacity Clock rate and power[edit] <span>The power consumption of SRAM varies widely depending on how frequently it is accessed; in some instances, it can use as much power as dynamic RAM, when used at high frequencies, and some ICs can consume many watts at full bandwidth. On the other hand, static RAM used at a somewhat slower pace, such as in applications with moderately clocked microprocessors, draws very little power and can have a nearly negligible power consumption when sitting idle – in the region of a few micro-watts. Several techniques have been proposed to manage power consumption of SRAM-based memory structures. [2] SRAM exists primarily as: general purpose products with asynchronous interface, such as the ubiquitous 28-pin 8K × 8 and 32K × 8 chips (often but not always named something along t







Your goal is to get your brand in front of as many eyes as possible. Yet, you need to sustain your farm campaign consistently, with depth and quality, and with a long-term vision in place. Keeping those costs and available resources in mind is important. The key? Market only to as many homes as your budget will allow, every month … and do so with RPR data.
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Look for areas that have a multitude of agents selling with no defined market share. Chances are the area isn’t being marketed heavily by any one agent, giving you an opportunity to consistently brand yourself as the local expert.
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Another option is to farm an area that has one exclusive agent with a dominant market share.
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SRAM is also used in personal computers, workstations, routers and peripheral equipment: CPU register files, internal CPU caches and external burst mode SRAM caches, hard disk buffers, router buffers, etc.
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eral megabytes may be used in complex products such as digital cameras, cell phones, synthesizers, etc. SRAM in its dual-ported form is sometimes used for realtime digital signal processing circuits. [citation needed] In computers[edit] <span>SRAM is also used in personal computers, workstations, routers and peripheral equipment: CPU register files, internal CPU caches and external burst mode SRAM caches, hard disk buffers, router buffers, etc. LCD screens and printers also normally employ static RAM to hold the image displayed (or to be printed). Static RAM was used for the main memory of some early personal computers such as




Start by saving your farm area. 1. Sign onto narrpr.com 2. Select All Properties from the menu option at the top of the search bar. 3. Search the area of your farm area by town, zip code, etc. 4. From the map tools, choose the polygon drawing pen to pinpoint your geographical farm. 5. Once you’ve connected the last point, choose Save and enter a name for your farm so that those boundaries are stored for easy access later on. From this point, you can search your saved farm name from the main search bar. 6. From there, filter your results using the left column variables, such as listing status, distressed, price range, living area, property type and sold date.
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Begin by tallying the number of sales in your farm area over the last 12 months.
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1. Type the name of your saved farm area directly into the All Properties search box. Then click Search 2. From the search results page, uncheck Active and Pending. 3. Select the Date Range radio button and enter beginning and ending dates. 4. Choose Apply to update the search and generate matches. 5. Next, for a period-to-period comparison, repeat the previous step by adjusting the Sold Date and compare the count of year-to-date sales with the same dates from the previous year.
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Real estate brokers will test you. They’ll first see if you buy the deals that they have in house that other investors have passed on.
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You must analyze each deal to separate the winners from the losers
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There is a tested recipe for buying an apartment complex.
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Use the tested recipe for deal creation. Follow simple rules and run certain calculations, and you’ll put quality deals into your portfolio.
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7. Create the Offer or Letter of Intent Once you’ve got a deal that you think is a winner, it’s time to make an offer on the property. If you are not making regular offers on properties—I’m talking one or two a week—you are really not in the game
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The offer does not mean you will definitely be buying the property. It means that you’re serious, and now want to see the real details behind the apartment complex
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When you are buying properties between 2 and 10 units, you will use a standard form to make your initial offer on the prop- erty.
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When you’re buying larger complexes, you will use a Letter of Intent.
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Throw the ball over to the seller’s court to either accept the offer or counter it. In most cases, the seller will counter the offer
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When you enter the negotiating process, you should position yourself so you can get to the best end result. That means following clear principles and steps
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determine at what maximum price you can buy the prop- erty. This is called the strike price. If you cannot get the seller down to this price, you then end the negotiations and move on to the next deal.
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with your marketing keeping your pipeline full, there is always another good deal around the corner.
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start negotiating at 10 percent below your strike price. Let’s say a property is on the market for $550,000. You do your analysis and determine that you won’t pay more than $500,000 for the property. That’s your strike price. If you follow the rule of thumb, you will start your negotiating at $450,000.
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Create and Sign the Purchase-and-Sale Agreement After the negotiation over price is complete, it’s time to create the purchase-and-sale agreement (also known as the P&S). This docu- ment outlines exactly how you will buy the property and what the key dates will be.
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The date on which both parties sign theP&Siscalled the effective date. All subsequent dates in the transaction are based on the effective date.
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You should either use your attorney’s P & S, or one that your attorney reviews and negotiates to protect your interests.
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It’s your attorney’s job to get that document to favor you as much as possible. Of course, that’s also the job of the attorney for the seller.
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Your attorney will analyze the document and come up with a list of exceptions: items and wording that are not in your best interest to have in the document. You’ll get a list of these exceptions and the negotiations will begin
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One common exception relates to key dates. Most deals allow 30 days for due diligence to be done and another 30 days to close the deal. This means you are closing the deal in 60 days. Be sure to surround yourself with a team that can meet this very short deadline, or you’ll lose deals to your competition. The person who offers the same amount of money—but gets that money into the seller’s pocket first—wins.
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Whenever you can, try to get 45 days for due diligence and another 45 days to close. Doing everything you need to do to close on an apartment complex—and doing it right—takes time. Still, stay alert to whether your competition is offering to close more quickly; you may have to cave on this point to save the deal.
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Another common negotiating point relates to the down payment. The seller will typically request between 1 percent and 5 percent for a down payment. The most common request for a smaller property is 3 percent to 5 percent, and for a larger complex, it’s 1 percent.
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This money is usually refundable until your due diligence period is over. At that point, it becomes hard, which means you can’t get it back. You must know your dates: Miss a date and possibly lose some money.
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Whenever possible, get a third party to hold the due diligence money (also known as the down payment or deposit). Your attorney is the best choice, but that rarely happens. The broker’s attorney or title company is usually the third party; sometimes the seller’s attorney will be required to hold the money. The one person who should never, ever, be allowed to hold the down payment money is the seller!
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another reason not to allow the seller to hold the down payment: It puts you in a weaker negotiating position.
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another negotiating point is the title work and the survey. In most cases, the seller usually pays for the title abstract work and for an updated survey of the property. More and more sellers are negotiating to have the buyer pay for these services.
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You will usually be required to send over the down payment money within 48 hours of signing yourP&S(orletter of intent).
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The P & S is the most important contract that you’ll sign before the closing. It’s well worth the money to have your attorney actively involved on your behalf
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Now that the ink is dry on the P & S, it’s time to start doing your due diligence, which is a Wall Street term for your in-depth property research. During your due diligence, you make sure that the deal you thought you were making an offer on is in fact the deal that exists.
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Due diligence is broken down into three categories: financial, phys- ical, and legal.
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The first information you usually get when doing your due dili- gence is financial. As should be stated in your P & S, the seller is required to forward to you all the financial information you need within 14 days.
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When this information comes in quickly, the deal usually goes smoothly. When it comes in late, or in bits and pieces, either the seller doesn’t keep very good records, or the seller is trying to hide something
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The information you’re requesting is: r Last three years of operating statements presented on a 12-month trend report r Year-to-date profit-and-loss statement r Balance sheet r Last 12 months rent roll
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We’re highly focused on the income aspects of the property, because you created your offer based on the income.
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f the seller can prove the income, great: The deal continues for- ward. If the seller can’t prove the income, it’s time to go back to the negotiating table. You want a lower price that makes sense with the new information you now have. Some sellers will agree to renego- tiate, and others won’t. You must be prepared to walk away.
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your marketing and deal flow are so vital.
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After you’ve confirmed the financial information, you can start on the rest of your due diligence. Do not start any other part of the due diligence process until the financials are done, because the physical and legal due diligence will begin to cost you money.
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If you walk away from the deal during the financial due diligence, the only money you have spent is your deposit, and you will get that back (assuming a third party is holding it, not the seller!). Any time during the due diligence period, if you decide for any reason that you want to be out of the deal, you get your deposit back.
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The first thing you do when you start your physical and legal due diligence is to hire a competent attorney to do the title work. The attorney will check that what you think you’re buying is in fact what you’re buying. He or she will review the legal description, previous owners, how the property was transferred previously, easements, and mineral rights. You’ll then receive a report. Either the deal is clean or it may have some issues that need to be resolved prior to closing. A good attorney will make sure that all issues are resolved before the closing. That way, when you resell the property, you won’t have any issues and you can collect your profit.
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You then hire a competent engineer to do the physical due dili- gence, which is a property inspection. The engineer will check all major mechanical and structural systems.
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The engineer will check all major mechanical and structural systems. On larger properties, he will do a survey of the apartment units. On smaller properties, he will go into every unit
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After you get the report, you’ll set up a time for you to walk through every single unit on the property—if you’re smart. I know this can take a while. I recently walked a 344-unit property with another member of my team. It took two days
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When you walk the units, what you’re looking for is the common problem. Every property has a common problem. It’s your job to find out what it is. Perhaps it’s the fact that all the faucets and handles are 20 years old and there are now repeated service calls to replace them, one by one. Maybe it’s outdated or worn carpet; it could be older appliances that will need to be replaced on a regular basis. It could be fraying cabi- net doors, leaking air conditioning units, or overflowing condensers. Every property has a common problem. Don’t stop until you find what it is, and allocate resources to counter that problem.
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While you’re doing your walk-throughs, you should be talking up the staff. You should find out who’s good or bad
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The engineer or inspector will have to provide you with key in- formation, such as what immediate repairs need to be done to the property, his estimate of costs, and, among other things, whether the property is properly zoned.
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If everything works out okay during the inspection phase, then you’re ready to get the financing.
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The inspection may have revealed problems that the seller didn’t tell you about. I don’t mean trivial stuff, which you can expect to find on every property. I’m talking about problems that will cost you a chunk of money: a bad boiler, a roof replacement, dry rot in the walls. If that’s the case, it’s time to renegotiate the Deal
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How to Get Your First Deal 37 valuable. But we were spending over $9 million for the property and I was using other investors’ money to buy the deal. I wanted to make sure I knew that property inside and out. When you walk the units, what you’re looking for is the common problem. Every property has a common problem. It’s your job to find out what it is. Perhaps it’s the fact that all the faucets and handles are 20 years old and there are now repeated service calls to replace them, one by one. Maybe it’s outdated or worn carpet; it could be older appliances that will need to be replaced on a regular basis. It could be fraying cabi- net doors, leaking air conditioning units, or overflowing condensers. Every property has a common problem. Don’t stop until you find what it is, and allocate resources to counter that problem. While you’re doing your walk-throughs, you should be talking up the staff. You should find out who’s good or bad, naughty or nice among those property personnel. They don’t realize it but they’re actually in a job interview. You may be buying that property. There is no better employee than one who knows the property well and does a good job. There’s no worse employee than one who knows the property well, and also knows how to slack off and steal from you. During this walk-through process, you should mentally put current employees into these two categories, subject to later confirmation, of course. The engineer or inspector will have to provide you with key in- formation, such as what immediate repairs need to be done to the property, his estimate of costs, and, among other things, whether the property is properly zoned. If everything works out okay during the inspection phase, then you’re ready to get the financing. The inspection may have revealed problems that the seller didn’t tell you about. I don’t mean trivial stuff, which you can expect to find in every property. I’m talking about problems that will cost you a chunk of money: a bad boiler, a roof replacement, dry rot in the walls. If that’s the case, it’s time to.... 11.
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Another term for renegotiating the deal is called retrading. If you plan on buying a lot of properties and doing a lot of business with key brokers, you don’t want to get the reputation of a retrader.
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These are investors who will nitpick a deal and try to squeeze every last dollar. Sellers hate them and so do brokers.
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Make doing business with you easy and you’ll do way more business.
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#contract
if something comes up that will cost you a chunk of cash, it’s time to go back to the seller and say: “Mr. Seller, you didn’t tell me that the boiler would need to be replaced. That’s a $15,000 job. I’d like you to give that money back out of the sales proceeds at closing. That sounds fair, doesn’t it?”
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Sometimes, you’ll find that your walking away will make the seller want you back. Other times, you’ll simply walk away.
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notice that I asked the seller to give the money back at the closing? That’s called a repair allowance.
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If you have the seller give it to you at closing, then your financing will be funding that repair. Banks usually allow you up to 3 percent of the purchase price for such repair allowances.
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#funding
You will finance your deals from three primary sources: local banks, national lenders, and conduits.
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Local banks are usually good for construction loans for multi- families. Their rates on regular loans are higher than other lenders, and their amortization schedule is usually shorter. (In other words, they want the money back sooner.) They typically write their loan over a 20-year period instead of a 25- or 30-year period. If you are doing a construction loan for a repositioning, you’ll need to use local lenders.
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banks won’t lend out of their geographical area for a repositioning; your only choice is the local guy.
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You’ll need a construction loan when repairs exceed 3 percent of the purchase price and you’re planning on financing the repairs into the deal.
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You’ll need a bridge loan when the property is less than 85 percent occupied. This occupancy level is called stabilization. You get your best loans at the lowest rates when you are buying stabilized properties. These properties also typically generate cash flow from Day One.
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call cash-flow-generating deals momentum plays because you have momentum in your favor. Your property is stabilized and cash flowing the day you buy it. National lenders and conduit lenders love these deals.
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National lenders are big enough that they don’t hold on to all the loans they make. Instead, they sell some of the deals to secondary markets. The key secondary market players are Fannie Mae (Federal National Mortgage Association) and Freddie Mac (Federal Home Loan Mortgage Corporation). They buy mortgages from the national lenders, so those lenders can now fund even more deals.
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Fannie Mae and Freddie Mac are great to do business with. They usually offer lower rates to close the deals, but they like their deals to be clean. They’re looking for stabilized properties. They don’t want to do a lot of repairs. One more thing: They like to see pitched roofs. They have a thing about flat roofs, because the flat design tends to result in more maintenance problems. They will finance properties that have them, but they won’t like it.
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We want to keep our lenders happy so they keep on lending to us! They also like to see an upward or stable trend in income for the last six months. This is called the six-month trailing report.
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You may want to finance through a conduit lender if: r Your deal is a little messy. r The numbers aren’t totally complete. r You’ve only started to stabilize over the last two to three months. r The property has a flat roof. A conduit lender gets its money from Wall Street, insurance com- panies, and investment houses. Conduit rates will be a little higher, but they’ll do deals that have a little edge to them.
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Hunchentoot is a web server written in Common Lisp and at the same time a toolkit for building dynamic websites. As a stand-alone web server, Hunchentoot is capable of HTTP/1.1 chunking (both directions), persistent connections (keep-alive), and SSL
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Hunchentoot - The Common Lisp web server formerly known as TBNL
Hunchentoot - The Common Lisp web server formerly known as TBNL [imagelink] Hunchentoot - The Common Lisp web server formerly known as TBNL Abstract Hunchentoot is a web server written in Common Lisp and at the same time a toolkit for building dynamic websites. As a stand-alone web server, Hunchentoot is capable of HTTP/1.1 chunking (both directions), persistent connections (keep-alive), and SSL. Hunchentoot provides facilities like automatic session handling (with and without cookies), logging, customizable error handling, and easy acces




Flashcard 1757666217228

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Hunchentoot provides facilities like automatic session handling (with and without cookies)
Answer
[default - edit me]

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill
Hunchentoot - The Common Lisp web server formerly known as TBNL
same time a toolkit for building dynamic websites. As a stand-alone web server, Hunchentoot is capable of HTTP/1.1 chunking (both directions), persistent connections (keep-alive), and SSL. <span>Hunchentoot provides facilities like automatic session handling (with and without cookies), logging, customizable error handling, and easy access to GET and POST parameters sent by the client. It does not include functionality to programmatically gener







Flashcard 1757687713036

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The net income figure is used to prepare the statement of [...]
Answer
retained earnings.

statusnot learnedmeasured difficulty37% [default]last interval [days]               
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scheduled repetition interval               last repetition or drill

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Open it
The net income figure is used to prepare the statement of retained earnings.

Original toplevel document

Subject 2. Major Financial Statements
recurring income is persistent. If an item in the unusual or infrequent component of income from continuing operations is deemed not to be persistent, then recurring (pre-tax) income from continuing operations should be adjusted. <span>The net income figure is used to prepare the statement of retained earnings. Balance Sheet A balance sheet provides a "snapshot" of a company's financial condition. Think of the balance sheet as a photo of the business at a sp







get a good mortgage broker on your team.
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Mort- gage brokers will have a stable of Fannie Mae, Freddie Mac, conduit, and local lenders that they do business with regularly.
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www.MultiFamily Millions.com and put in the keyword broker.
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Choose a Management Company While all this is going on, you should also be lining up your man- agement company.
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irem.org web site. IREM stands for the Institute of Real Estate Management. Go to this site and look for Certified Property Managers (CPMs) or Accredited Residential Managers (ARMs) in your area.
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Property managers specialize in certain properties. Make sure you match the property manager with your property type.
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This company was indeed expert at managing high-end properties. But mine was a low-end property. They didn’t know how to attract that type of tenant base, and were over-screening the tenants. They also were repairing my vacant units as if the CEO of a company was going to move in. When I asked them about this, they told me: “We have high stan- dards, and we aren’t going to compromise them.” I told them that I, too, had certain standards, the first being that I make a profit while providing a safe, affordable, and clean place to live. If I don’t make the profit, I can’t provide the housing.
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Close the Deal All the pieces are now in place. The only thing left to do is to finish the financing paperwork. You are ready to close the deal. When you buy smaller properties, you’ll close in the title office or an attorney’s office.
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With bigger complexes in emerging markets across the United States, the lender will mail you a document package overnight. You’ll sign it in front of a notary, and send it back overnight.
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The seller will do the same. Then you wire the funds over on the appropriate day and you’re the proud owner of the property. You now turn it over to the management company.
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Buy and Flip When you’re starting out, you have very little time and less money. One option, therefore, is to flip your deal for a quick profit. When I say flip, I mean you put a property under contract, close on it, and immediately sell it to another party to realize your profits.
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To flip a property, you must be buying the property under market value and you then resell it at market value to another investor.
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Why would people sell a property to you below the market value? There are many reasons: r They may have inherited a property they don’t want or don’t know how to run. r They’re in foreclosure. r They could be in bankruptcy. r They’re a burned-out landlord. r They see profits starting to drop and want to get out while they still can. r It may be an estate sale. r They could be trading up to a bigger property. r They’re retiring from the game. r They need money quickly to fund another venture. r They need money even more quickly to pay taxes to the IRS. People sell below market value for these reasons and more.
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I want systems in place to attract these motivated sellers continuously.
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The mortgage amount is $311,000. You agree to purchase the property for $311,000. You could make your profit on this property in two ways: 1. You could assign the property to another investor and get an assignment fee, or 2. You could close on the property and immediately put it back on the market to resell it
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The Assignment Process Let’s look at how the assignment approach works: When you create the offer to buy the property, you put your entity name in as the buyer of the property. (Never buy in your own name, for asset-protection purposes.) After your entity name, you put the phrase: and/or assigns.
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when I’m buying a property, I usually buy in a limited liability company (LLC). For simplicity, I usually call the LLC by the same name as the street address of the property.
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if I buy a property on Market Street, I name the property Market LLC.
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If I’m purchasing the 284-unit Mag- nolia Park apartment complex, I name it Magnolia Park LLC.
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be sure that whatever name you give to the LLC, add to the end: and/or assigns. This allows you to assign the contract to a third party. You will receive an assignment fee before any closing, and the third party will close on the property. The benefit to you? It’s the very fastest way to get money after putting a deal together. The downside is you don’t get the big lump sum that might be yours from the property down the road.
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The size of your assignment fee depends on how well you negoti- ated the deal, and how much equity is in it. On smaller properties, most investors will not buy from you unless they’re making at least $20,000 on the transaction. That’s the low end. Thus, if you want to make a $5,000 assignment fee, you’ll need at least $25,000 in equity. When I say equity, I mean the net amount of proceeds in the deal after taking the market value and deducting any costs associated with it.
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Most assignment fees are between $5,000 and $10,000 on smaller deals and as much as $100,000 to $500,000 on bigger ones. Not bad, huh.
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A $52 million portfolio. The person holding the contract is willing to wait for his $1.2 million until after we close. That’s good, because I can now finance that right into the deal
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When you are assign- ing a contract over to a third party, never wait until the closing to get your assignment fee!
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We do not sell the same way we buy. You should not wait because you want your buyer to have some skin in the game. You want him to put up cash so there is a high probability he will close.
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Subject 1. The Objective of Financial Reporting
#reading-estandarte

An awareness of the reporting framework underlying financial reports can assist in security valuation and other financial analysis. This framework describes the objectives of financial reporting, desirable characteristics for financial reports, the elements of financial reports, and the underlying assumptions and constraints of financial reporting. An understanding of the framework that is broader than knowledge of a particular set of rules offers an analyst a basis from which to infer the proper financial reporting, and thus security valuation implications, of any financial statement element transaction.

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you want the seller to pay the assignment fee beforehand: If he doesn’t, he may decide to renegotiate with you as you are getting close to the closing. If this happens, you’ll be negotiating from weakness: You need him to close to get that deal done and get your money.
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The only time you should assign a deal is if you need money quickly, or you’re so busy doing other deals that you don’t have time to do anything more with this one.
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stick with the deal and get that pot of gold that’s waiting at the end of the rainbow. The way to do that is to take the deal through closing, and then sell at the market rate. So instead of having to assign the deal to someone who will make his profit by selling it at market rate, you’ll get that profit, too. It will mean that you have to arrange your financing, and close, and then prep the property for resale (most likely cosmetic repairs). This is still a flip, because you’re not holding on to the property for any length of time. It’s just that for your work in closing the deal, you get more profit.
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begin the marketing process to sell that property as soon as you get it under contract. Not after you own it, but just after you have it under contract.
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Buy your prop- erty with good enough numbers in place that it’s generating cash flow. That way, you won’t be coming out of pocket to hold the property before you sell.
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With an empty single-family house, you pay the mortgage until it’s sold. I don’t like that. With a multi-family property, your tenants pay your mortgage and expenses until you sell it.
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Buy and Hold If you get past that phase where all you can think about is a wad of fast cash, then the next goal is to generate cash every month.
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If you think you can create additional value in the property through market appreciation, then hold it for a while (usually one to five years). There must be certain factors present in the market (like impressive job growth) that will create additional demand for properties. This is the essence of the emerging-market strategy
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While you’re holding the property, you’ll run it like a business. A qualified property management company will run the property. You’ll check financial and operational performance every month. If your management company is doing a good job, you’ll also cash checks every month!
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While you’re holding the property, it’s important that you are always raising rents. We call this pushing rents. If you’re in the right market at the right time, rents should be rising. Every time you rent a vacant unit or do a lease renewal, raise the rents to whatever the market will bear. Doing this will increase your net operating income. That, in turn, will increase the value of your property. If you are disciplined at this, you will see your equity increase very rapidly.
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You are not raising rents; it’s your manager who’s doing it!
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At some point, it will be time to sell the property and trade up to a bigger property in that market, or something in another emerging market.
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Here is an example of this strategy in action: I bought a 32-unit property in Huntsville, Alabama, for $614,000. At the time, Huntsville was an emerging market. I held the property for 18 months and resold it for $1,100,000. After all costs, the profit was close to $430,000.
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I had a property manager run the building. I would get my profit-and-loss statement every month, along with a cash flow check.
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It’s all about turning your small properties into big properties, and your big properties into bigger properties!
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Buy, Reposition, and Sell After your investing has built a solid financial foundation for you, you’ll want to make some real money. If you’re willing to do the work it takes, then you should buy, reposition, and sell.
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Repositioning is when you buy a property with a problem, fix that problem, and resell the property for a big profit.
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You cannot only reposition a property, but also the tenant base. When you reposition, you add value.
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When talking with bro- kers, ask them if they have any value add deals. They’ll know exactly what you mean; they’ll also know by that code word that you’re a player!
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You can add value by raising rents, raising occupancy, doing repairs, increasing income, decreasing expenses, and many other ways.
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To reposition the tenant base, you change tenants over time to a profile that is best suited for the property.
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Let’s say you have a 20-unit apartment building that was built 30 years ago. Because of its age, let’s say it’saCproperty. Occupancy has dropped to 77 percent and rents are low. They’re doing anything they can to keep the old tenants, so they are not raising rents. That’s causing a lot of deferred maintenance on the property (that is, repairs that need to be done and have been neglected). It’s hard to get new tenants to move in because the place doesn’t look good. You can see, of course, the vicious cycle: Because they can’t get new tenants to move in, they don’t have the cash to do repairs. Their vacancy drops even more. This is the situation at a lot of properties in need of help.
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You look at the deal and realize that the property actually sits in a good B area. You decide you want to take a crack at repositioning it for big profits. The property is selling for $550,000 and you think you can resell it for $950,000 when you’re done.
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You’ll need to repair the interior and exterior of the property. You won’t break the bank on the quality of the work, but will install fixtures and appliances that a B tenant would expect to find. Hence, you are repositioning this C property to a B and shooting to reposition the tenant base from a C tenant to a B tenant.
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follow a well-tested process to reposition with the greatest profit. First, you repair the exterior, the common areas (recreation hall, patio, and so forth), and change the name of the property, adding new signage.
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For a repositioning to be successful, you must first change the per- ception of the property in the eyes of both the current tenant base and the community. By changing the appearance of the outside of the property, you’ve taken the first highly visible step to changing that perception. You also put up big banners that say Under New Management, and New Management, New Attitude.
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The strategy is to keep the current tenants paying rent as long as possible, because you need this money for cash flow. But you realize that only 20 percent to 30 percent will still be living in the property one year from the day you start. This doesn’t mean you will lose 70 percent to 80 percent of your occupancy; instead, you’ll be trading up your tenants. The old tenant profile will move out, and the new profile will move in.
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Repositions fail for two reasons: 1. The buyer runs out of money; or 2. The buyer hires the wrong management company.
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When doing your calculations, first determine how much the re- pairs will cost. Then determine what your breakeven occupancy is. Do this by taking the total amount of expenses you have on the property, including your debt service (that is, the mortgage). Then calculate your average market rent and divide the average rent by your total expenses. That’s your breakeven annual rent. Divide that number by 12 and you are now looking at your monthly breakeven rent.
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Let’s say you have a 30-unit building and your annual expenses, including debt service, is $175,000. Divide that number by 12 to get a monthly expense figure of $14,583. Now divide the $14,583 by the average monthly rent ($650) and you get 22.4. Round that up to 23. This means if you rent 23 units, you will be at breakeven.
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FASB
#reading-estandarte

Financial Accounting Standards Board (FASB)

The FASB is a non-governmental body that sets accounting standards for all companies issuing audited financial statements. All FASB pronouncements are considered authoritative; new FASB statements immediately become part of GAAP.

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#reading-estandarte

Audited financial statements, related footnotes, and supplementary data are presented in both annual reports sent to stockholders and those filed with the SEC. These filings often contain other valuable information not presented in stockholder reports.

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To find out what percent occupancy this represents, simply divide the breakeven number needed by the total number of units: 23/30 = .766. This means you need to get to 77 percent occupancy to break even. Occupancy above that will generate positive cash flow.
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let’s say you’re buying this building at 65 percent occupancy. You need to figure out how long it will take you to repair the property so you can start leasing it up. Then figure how many units you can lease per month.
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At 65 percent occupancy, this means you have about 20 units rented. To get to your 23-unit breakeven number, you’ll have to rent an additional three units.
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Now you’re buying a 300-unit property. Your breakeven is 230 units. If you are buying it at 65 percent then you have 200 units occupied. You must now lease up 30 units. You must figure out how many units you can lease up each month. Let’s say that number works out to be five. If you need 30 units rented, it’s going to take you a minimum of six months to get there (30 divided by 5). Now add on how long it will take you to do the repairs and change the perception. Finally, add a couple of more months. (How often do things go perfectly?) You need six months to lease up, three months to do repairs, and a fudge factor of three months. That’s a whole year before you get to break even. The question is, do you have enough money to cover expenses for that year until you get there?
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Repositions can be cash cows when investors go in with their eyes open and a realistic reserve. They can be disasters when they blunder in without doing the math
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How often does a rehab come in at or below budget? So add at least another 10 percent to the cost of your rehab. By doing all of this, you will set yourself up for success.
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Qualitative Characteristics of Financial Statements
#reading-estandarte
  • Financial information faithfully represents transactions and events when accounted for in accordance with their substance and economic reality and not merely their legal form. Commonly, a legal agreement will purport that a company has "sold" assets to a third party. However, an analysis of the substance of the arrangement indicates that the company retains control over the future economic benefits and risks embodied in the asset, and should continue to recognize it on its own balance sheet.

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Qualitative Characteristics of Financial Statements
#reading-estandarte
  • Financial information is reliable if it is free from material error and
    is complete. Information is material if its omission or misstatement could influence decisions that end-users make on the basis of the financial statements. Information is reliable when it is neutral or free from bias and prudence. A degree of prudence when preparing financial information enhances its reliability. However, a company should not use prudence as the basis for the recognition of, for example, excessive provisions.

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Qualitative Characteristics of Financial Statements
#reading-estandarte
  • End-users must be able to compare a company's financial statements through time in order to identify trends in financial performance (comparability). Hence, policies on recognition, measurement, and disclosure must be applied consistently over time. Where a company changes its accounting for the recognition or measurement of transactions, it should disclose the change in the Basis of Accounting section of its financial statements and follow the guidance set out in IFRS.

    The application of qualitative characteristics and accounting standards usually results in financial statements that show a true and fair view, or fairly present a company's financial position and performance.

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Flashcard 1757945400588

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Show Interfaces


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Most important show commands for CCENT - 16985 - The Cisco Learning Network
est and since show commands are so important, I'm adding their own section. These are the ones I have so far, I've tried to group them according to their role in troubleshooting. Can you guys think of any others I might need on the CCENT? <span>Show Interfaces show ip interface brief show mac address-table show ip protocols show ip route show cdp neighbors show cdp neighbors detail show cdp interface show running-config show version