# on 15-Feb-2018 (Thu)

#### Flashcard 1428510084364

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#algebra-baldor
Question
Las cantidades conocidas se expresan por [...]
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

Tags
#48-laws-of-power
Question
Half of the game is learning how to [...] that eat away at you and cloud your reason.
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

Tags
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?
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 [...] .
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

#### Annotation 1729501203724

 #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.

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)

#### Annotation 1729503300876

 #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

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

#### Annotation 1729504873740

 #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

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

#### Annotation 1729506970892

 #multivariate-normal-distribution In the bivariate case the expression for the mutual information is:

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

#### Annotation 1729523485964

 #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...

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] #### Annotation 1729525845260  #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] status not read 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 #### Annotation 1729527942412  #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 + Bμ and variance BΣBT . Corollaries: sums of Gaussian are Gaussian, marginals of Gaussian are Gaussian. status not read 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 ) #### Annotation 1729530039564  #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. status not read 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 #### Annotation 1729532136716  #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. status not read 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 #### Annotation 1729534496012  #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. status not read 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 #### Annotation 1729578011916  #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. status not read 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 .

#### Original toplevel document

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 [...] .
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

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

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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

#### 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 [...]
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 [...]
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 [...]

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

#### Annotation 1729678413068

 #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

#### Original toplevel document

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]

#### Flashcard 1729680772364

Tags
#multivariate-normal-distribution
Question

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

#### Original toplevel document

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]

#### Flashcard 1729692830988

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#multivariate-normal-distribution
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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:

#### Original toplevel document

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

#### Flashcard 1729696763148

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#multivariate-normal-distribution
Question
The mutual information of a distribution is a special case of the Kullback–Leibler divergence in which is [...] and is [...]
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

#### Original toplevel document

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

#### Flashcard 1729699122444

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#multivariate-normal-distribution
Question
The multivariate normal distribution is often used to describe correlated real-valued random variables each of which [...]
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

#### Original toplevel document

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

#### Flashcard 1729700695308

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#multivariate-normal-distribution
Question
a random vector is said to be k-variate normally distributed if [...] has a univariate normal distribution.
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.

#### Original toplevel document

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)

#### Annotation 1738538093836

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

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 <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

#### Flashcard 1738588949772

Tags
#multivariate-normal-distribution
Question
If [...], then the multivariate normal distribution is degenerate and does not have a density.
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.

#### Original toplevel document

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 <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

#### Flashcard 1751346187532

Tags
#investopedia
Question
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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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.

#### Original toplevel document

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

#### Annotation 1757308128524

 I don’t consider myself in the real estate business! I’m in the marketing business.

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#### Annotation 1757309701388

 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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#### Annotation 1757311536396

 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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#### Annotation 1757313109260

 Have a whole bunch of marketing tools to apply to any market at any time.

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#### Annotation 1757316779276

 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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#### Annotation 1757319138572

 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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#### Annotation 1757400927500

 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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#### Annotation 1757403286796

 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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#### Annotation 1757405121804

 Property Resource ® (RPR ® ) will provide all of the data and reports you need to execute a profit-yielding endeavor.

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#### Annotation 1757406956812

 A predetermined set of criteria for establishing your farm area will help save time and energy

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#### Annotation 1757408529676

 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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#### Annotation 1757410364684

 know how to calculate turnover

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#### Annotation 1757411937548

 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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#### Annotation 1757413510412

 Look to RPR heat maps to determine whether values in your farm area are increasing or decreasing over time.

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#### Annotation 1757416393996

 find the 12-month change in estimated values, list vs sales prices, and the density of distressed properties

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#### Annotation 1757428976908

 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.

Static random-access memory - Wikipedia
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

#### Flashcard 1757431074060

Question
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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 Advantages: Low power consumption Simplicity – a refresh circuit is not needed Reliability Disadvantages: Price Capacity Clock rate and power <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

#### Annotation 1757432646924

 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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#### Annotation 1757434219788

 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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#### Annotation 1757435792652

 Another option is to farm an area that has one exclusive agent with a dominant market share.

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#### Annotation 1757437365516

 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.

Static random-access memory - Wikipedia
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 <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

#### Annotation 1757438938380

 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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#### Annotation 1757441035532

 Begin by tallying the number of sales in your farm area over the last 12 months.

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#### Annotation 1757442608396

 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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#### Annotation 1757446278412

 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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#### Annotation 1757447851276

 You must analyze each deal to separate the winners from the losers

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#### Annotation 1757449424140

 There is a tested recipe for buying an apartment complex.

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#### Annotation 1757450997004

 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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#### Annotation 1757453356300

 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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#### Annotation 1757456239884

 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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#### Annotation 1757458599180

 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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#### Annotation 1757460172044

 When you’re buying larger complexes, you will use a Letter of Intent.

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#### Annotation 1757462007052

 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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#### Annotation 1757464366348

 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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#### Annotation 1757465939212

 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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#### Annotation 1757470919948

 with your marketing keeping your pipeline full, there is always another good deal around the corner.

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#### Annotation 1757547203852

 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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#### Annotation 1757549563148

 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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#### Annotation 1757551136012

 Make doing business with you easy and you’ll do way more business.

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#### Annotation 1757757181196

 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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#### Annotation 1757758754060

 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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#### Annotation 1757760326924

 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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#### Annotation 1757761899788

 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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#### Annotation 1757767929100

 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.

#### Annotation 1757770288396

 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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#### Annotation 1757771861260

 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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#### Annotation 1757773696268

 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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#### Annotation 1757775531276

 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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#### Annotation 1757777104140

 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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#### Annotation 1757778677004

 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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#### Annotation 1757780512012

 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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#### Annotation 1757782084876

 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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#### Annotation 1757783657740

 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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#### Annotation 1757785230604

 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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#### Annotation 1757787065612

 You are not raising rents; it’s your manager who’s doing it!

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#### Annotation 1757788638476

 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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#### Annotation 1757819571468

 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.

#### Annotation 1757822192908

 #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.

#### Annotation 1757823503628

 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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#### Annotation 1757825076492

 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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#### Annotation 1757826911500

 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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#### Annotation 1757828484364

 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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#### Annotation 1757830057228

 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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#### Annotation 1757831630092

 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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#### Annotation 1757840542988

 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.

#### Annotation 1757868330252

 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.

#### Annotation 1757875408140

 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.

#### Flashcard 1757945400588

Question
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