# on 28-Jul-2017 (Fri)

#### Flashcard 1426270326028

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#cfa #cfa-level-1 #economics #microeconomics #reading-13-demand-and-supply-analysis-introduction #study-session-4
Question
[...] are achieved simultaneously, and as long as neither the supply curve nor the demand curve shifts, there is no tendency for either price or quantity to vary from those values.
equilibrium price and quantity

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equilibrium price and quantity are achieved simultaneously, and as long as neither the supply curve nor the demand curve shifts, there is no tendency for either price or quantity to vary from their equilibrium values

#### Original toplevel document

3. BASIC PRINCIPLES AND CONCEPTS
ity. Alternatively, when the quantity that buyers are willing and able to purchase at a given price is just equal to the quantity that sellers are willing to offer at that same price, we say the market has discovered the equilibrium price. So <span>equilibrium price and quantity are achieved simultaneously, and as long as neither the supply curve nor the demand curve shifts, there is no tendency for either price or quantity to vary from their equilibrium values. <span><body><html>

#### Flashcard 1431907994892

Tags
#cfa #cfa-level-1 #economics #microeconomics #reading-13-demand-and-supply-analysis-introduction #study-session-4
Question
Does the Law of demand hold in all circumstances.
Nein

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d><head>In general, economists believe that as the price of a good rises, buyers will choose to buy less of it, and as its price falls, they buy more. This is such a ubiquitous observation that it has come to be called the law of demand , although we shall see that it need not hold in all circumstances.<html>

#### Original toplevel document

3.1. The Demand Function and the Demand Curve
head> We first analyze demand. The quantity consumers are willing to buy clearly depends on a number of different factors called variables. Perhaps the most important of those variables is the item’s own price. In general, economists believe that as the price of a good rises, buyers will choose to buy less of it, and as its price falls, they buy more. This is such a ubiquitous observation that it has come to be called the law of demand , although we shall see that it need not hold in all circumstances. Although a good’s own price is important in determining consumers’ willingness to purchase it, other variables also have influence on that decision, such as consumers’ inco

#### Flashcard 1436084997388

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Question
analysts may appraise the quality of the company’s capital budgeting process on the basis of whether the company has an [...] or an [...]
accounting focus

economic focus.

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analysts may appraise the quality of the company’s capital budgeting process on the basis of whether the company has an accounting focus or an economic focus.

#### Original toplevel document

1. INTRODUCTION
of maximizing shareholder value. Because capital budgeting information is not ordinarily available outside the company, the analyst may attempt to estimate the process, within reason, at least for companies that are not too complex. Further, <span>analysts may be able to appraise the quality of the company’s capital budgeting process—for example, on the basis of whether the company has an accounting focus or an economic focus. This reading is organized as follows: Section 2 presents the steps in a typical capital budgeting process. After introducing the basic principles of capital budgeti

#### Flashcard 1438920084748

Tags
#cfa #cfa-level-1 #economic-and-normal-profit #economics #microeconomics #reading-15-demand-and-supply-analysis-the-firm #section-2-objectives-of-the-firm #study-session-4
Question

Economic profit for a firm can originate from sources such as:

• difficult to [...]

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Economic profit for a firm can originate from sources such as: competitive advantage; exceptional managerial efficiency or skill; difficult to copy technology or innovation (e.g., patents, trademarks, and copyrights); exclusive access to less-expensive inputs; fixed supply of an output, commodity, or resource; preferential treatment under governmental p

#### Original toplevel document

2. OBJECTIVES OF THE FIRM

#### Flashcard 1621399571724

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#tvm
Question
If a bank states that a particular CD pays a rate of 3% that compounds 4 times a year this is an example of what kind of rate?
Periodic interest rate

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#### Flashcard 1635123596556

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#statistical-concepts-and-market-returns
Question

In Step 4 of a Frequency Distribution, when rounding the interval width, [...].

round up rather than down

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#### Annotation 1641088421132

The arithmetic mean is a special case of the weighted mean in which all the weights are equal to 1/n.

#### Annotation 1644436262156

We can find a portfolio’s variance as a straightforward function of the variances and correlations of the component securities.

We cannot do it for semivariance and target semivariance.

We also cannot take the derivative of semivariance or target semivariance.

Will be disscussed in probability.

#### Annotation 1644471651596

Although CV was designed as a measure of relative dispersion, its inverse reveals something about return per unit of risk.

For example, a portfolio with a mean monthly return of 1.19 percent and a standard deviation of 4.42 percent has an inverse CV of 1.19%/4.42% = 0.27. This result indicates that each unit of standard deviation represents a 0.27 percent return.

#### Flashcard 1644493409548

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Question

What happens to a portfolio's positive Sharpe ratio if we increase risk

Sharpe ratio decreases if we increase risk, all else equal

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#### Annotation 1644544003340

In calculations of variance since the deviations around the mean are squared, we do not know whether large deviations are likely to be positive or negative.

#### Flashcard 1644733795596

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Question
What would you use to compute the growth rate of a financial variable such as earnings or sales, given a set of info?
The geometric mean return

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#### Annotation 1644783865100

In calculations of variance we do not know whether large deviations are likely to be positive or negative, hence the degree of symmetry in return distributions.

#### Flashcard 1644973657356

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Question
The [...] for every class is the greatest value possible in that class.
upper limit

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#### Flashcard 1644975492364

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Question
Class boundaries are the [...]
numbers used to separate classes.

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#### Flashcard 1645248122124

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#edx-probability
Question
Putting together a probabilistic Model involves two steps:

First step, we describe the [...]

Second step, we describe [...]
possible outcomes of the phenomenon or experiment

our beliefs about the likelihood of the different possible outcomes

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Lesson 1. Sample space
Putting together a probabilistic Model that is, a model of a random phenomenon or a random experiment involves two steps. First step, we describe the possible outcomes of the phenomenon or experiment of interest. Second step, we describe our beliefs about the likelihood of the different possible outcomes by specifying a probability law. Here, we start by just talking about the first step, namely, the description of the possible outcomes of the experiment. So we carry out an experiment. For example

#### Flashcard 1645253102860

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#edx-probability
Question
A set of outcomes in an experiment is denoted by [...]
$$\Omega$$

Capital omega

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Lesson 1. Sample space
ng a list of the possible outcomes-- or, a better word, instead of the word "list", is to use the word "set", which has a more formal mathematical meaning. So we create <span>a set that we usually denote by capital omega. That set is called the sample space and is the set of all possible outcomes of our experiment. The elements of that set should have certa

#### Annotation 1645606210828

It is noteworthy that Muhammad b, Habib (cL 245/860), the transmitter of Jarir's diwan, attempts to solve this problem in Jarir's naqida by claiming that the poem was composcd in two stages. The first part, which does not include any reference to Jarir's poetic rival and which according to Kitab al-aghani was recited in the presence of Muawiya, was composed about 20 years before the second part, However, this statement is doubtful also because it includes incorrect data about the poem.

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#### Annotation 1645611977996

It is very clear that during this period of composing naqa’id poetry, although poets used to recite their poems in al-Kunasa, it was not the place where the naqa’id poetry of Jarir and his opponents were presented. It seems that the two poets, Jarir and Ghassan, and apparently also the other poets that attempted to help Ghassan, recited their naqa’idas in al-Yamama itself.

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#### Annotation 1645643959564

Based on a view of writing as a social and communicative engagement between writer and reader, metadiscourse focuses our attention on the ways writers project themselves into their discourse to signal their attitude towards both the content and the audience of the text

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#### Annotation 1645807537420

To find a box-and-whisker plot of order data we find the median and, to divide the data into quarters, we then find the medians of these two halves.

;:"","st":"Khan Academy","th":126,"tu":"https://encrypted-tbn0.gstatic.com/images?q\u003dtbn:ANd9GcSn5LucwU2YqqP-QbKVKFxZQrH67dnFFkLdw7mMGEhss07jzQixQxdTCiUW","tw":224} <span>To create a box-and-whisker plot, we start by ordering our data (that is, putting the values) in numerical order, if they aren't ordered already. Then we find the median of our data. The median divides the data into two halves. To divide the data into quarters, we then find the medians of these two halves. Box-and-Whisker Plots - Purplemath www.purplemath.com/modules/boxwhisk.htm Feedback About this result People also ask What can you tell from a box and whisker plot?

#### Annotation 1645852364044

If we multiply the S&P 500 first forecast by the probability of expansion and the second forecast by the probability of contraction and then add these weighted forecasts, we are calculating the expected value of the S&P 500 at year-end.

Expected Value-Weighted mean
Suppose we make one forecast for the year-end level of the S&P 500 assuming economic expansion and another forecast for the year-end level of the S&P 500 assuming economic contraction. If we multiply the first forecast by the probability of expansion and the second forecast by the probability of contraction and then add these weighted forecasts, we are calculating the expected value of the S&P 500 at year-end. If we take a weighted average of possible future returns on the S&P 500, we are computing the S&P 500’s expected return.

#### Annotation 1645854723340

If we take a weighted average of possible future returns on the S&P 500, we are computing the S&P 500’s expected return.

Expected Value-Weighted mean
traction. If we multiply the first forecast by the probability of expansion and the second forecast by the probability of contraction and then add these weighted forecasts, we are calculating the expected value of the S&P 500 at year-end. <span>If we take a weighted average of possible future returns on the S&P 500, we are computing the S&P 500’s expected return. <span><body><html>

#### Flashcard 1645856558348

Tags
#investopedia
Question
[...] is an investment technique of buying a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price.
Dollar-cost averaging (DCA)

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Dollar-cost averaging (DCA) is an investment technique of buying a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price. The investor purchases more shares when prices are low and fewer shares when prices are high. The premise is that DCA lowers the average share cost over time, increasing the opportunity

#### Original toplevel document

Dollar-Cost Averaging (DCA)
What is 'Dollar-Cost Averaging - DCA' <span>Dollar-cost averaging (DCA) is an investment technique of buying a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price. The investor purchases more shares when prices are low and fewer shares when prices are high. The premise is that DCA lowers the average share cost over time, increasing the opportunity to profit. The DCA technique does not guarantee that an investor won't lose money on investments. Rather, it is meant to allow investment over time instead of investment as a lump sum. BREAKING DOWN 'Dollar-Cost Averaging - DCA' Fundamental to the strategy is a commitment to investing a fixed dollar amount each month. Depending

#### Flashcard 1645860228364

Question

According to Chebyshev’s inequality, for any distribution with finite variance, the proportion of the observations within k standard deviations of the arithmetic mean is at least [...] for all k > 1.

1 − 1/k2

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According to Chebyshev’s inequality, for any distribution with finite variance , the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 − 1/k 2 for all k > 1.

#### Flashcard 1645861801228

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Question
CV was designed as a measure of relative dispersion but its inverse reveals something about [...]
return per unit of risk

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Although CV was designed as a measure of relative dispersion, its inverse reveals something about return per unit of risk because the standard deviation of returns is commonly used as a measure of investment risk. For example, a portfolio with a mean monthly return of 1.19 percent and a standard deviation

#### Flashcard 1645865209100

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Question
A portfolio with a mean return of 1.19% and a standard deviation of 4.42% has an inverse CV of $$\frac{0.0119}{0.0442}=0.27$$. This result indicates that [...] represents [...]
each unit of standard deviation represents a 0.27 percent return.

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Open it
Although CV was designed as a measure of relative dispersion, its inverse reveals something about return per unit of risk. For example, a portfolio with a mean monthly return of 1.19 percent and a standard deviation of 4.42 percent has an inverse CV of 1.19%/4.42% = 0.27. This result indicates that each unit of standard deviation represents a 0.27 percent return.

#### Flashcard 1645869403404

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Question
In calculations of variance since the deviations around the mean are squared, we do not know whether [...]
large deviations are likely to be positive or negative.

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Open it
In calculations of variance since the deviations around the mean are squared, we do not know whether large deviations are likely to be positive or negative.

#### Flashcard 1645875432716

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Question
The arithmetic mean is a special case of the weighted mean in which all the weights are equal to [...]
1/n.

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The arithmetic mean is a special case of the weighted mean in which all the weights are equal to 1/n.

#### Annotation 1645877005580

suppose that the portfolio manager maintains constant weights of 60 percent in stocks and 40 percent in bonds for all five years. This method is called a constant-proportions strategy.

Open it
Now suppose that the portfolio manager maintains constant weights of 60 percent in stocks and 40 percent in bonds for all five years. This method is called a constant-proportions strategy. Because value is price multiplied by quantity, price fluctuation causes portfolio weights to change. As a result, the constant-proportions strategy requires rebalancing to restore the w

#### Flashcard 1645880413452

Tags
#math-shit
Question
How many digits can the stems in a stemplot have?
As many as needed

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The stem of a stemplot can have as many digits as needed, but the leaves should contain only one digit.

#### Original toplevel document

Stem-and-leaf graph
Suppose you have the following set of numbers (they might represent the number of home runs hit by a major league baseball player during his career). 32, 33, 21, 45, 58, 20, 33, 44, 28, 15, 18, 25 <span>The stem of a stemplot can have as many digits as needed, but the leaves should contain only one digit. To create a stemplot to display the above data, you must first create the stem. Since all of the numbers have just two digits, start by arranging the tens digits from

#### Flashcard 1645882772748

Tags
#math-shit
Question
How many digits can the leaves of a stemplot have?
only one digit.

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#### Parent (intermediate) annotation

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The stem of a stemplot can have as many digits as needed, but the leaves should contain only one digit.

#### Original toplevel document

Stem-and-leaf graph
Suppose you have the following set of numbers (they might represent the number of home runs hit by a major league baseball player during his career). 32, 33, 21, 45, 58, 20, 33, 44, 28, 15, 18, 25 <span>The stem of a stemplot can have as many digits as needed, but the leaves should contain only one digit. To create a stemplot to display the above data, you must first create the stem. Since all of the numbers have just two digits, start by arranging the tens digits from

Article 1645885132044

Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur

If we have two events, A and B, that we are interested in, we often want to know the probability that either A or B occurs. Note the use of the word "or," the key to this rule. The "or" is what we call an "inclusive or." In other words, either one event can occur or both events can occur. Such probabilities are calculated using the addition rule for probabilities. P(A or B) = P(A) + P(B) - P(AB) The logic behind this formula is that when P(A) and P(B) are added, the occasions on which A and B both occur are counted twice. To adjust for this, P(AB) is subtracted. If events A and B are mutually exclusive, the joint probability of A and B is 0. Consequently, the probability that either A or B occurs is simply the sum of the unconditional probabilities of A and B: P (A or B) = P(A) + P(B). What is the probability that a card selected from a deck will be either an ace or a spade? The relevant probabilities are: P(ace) = 4/52; P(spade) = 13/52 The only way in which an

#### Annotation 1645886704908

If we have two events, A and B, that we are interested in, we often want to know the probability that either A or B occurs. Note the use of the word "or," the key to this rule. The "or" is what we call an "inclusive or." In other words, either one event can occur or both events can occur.

Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur
If we have two events, A and B, that we are interested in, we often want to know the probability that either A or B occurs. Note the use of the word "or," the key to this rule. The "or" is what we call an "inclusive or." In other words, either one event can occur or both events can occur. Such probabilities are calculated using the addition rule for probabilities. P(A or B) = P(A) + P(B) - P(AB) The logic behind this f

#### Flashcard 1645888277772

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Question

P(A or B) = P(A) + P(B) - P(AB)

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Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur
use of the word "or," the key to this rule. The "or" is what we call an "inclusive or." In other words, either one event can occur or both events can occur. Such probabilities are calculated using the <span>addition rule for probabilities. P(A or B) = P(A) + P(B) - P(AB) The logic behind this formula is that when P(A) and P(B) are added, the occasions on which A and B both occur are counted twice. To adjust for this, P(AB) is subtracted. &#

#### Flashcard 1645890637068

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Question
If events A and B are mutually exclusive, the joint probability of A and B is [...]
0.

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Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur
P(A or B) = P(A) + P(B) - P(AB) The logic behind this formula is that when P(A) and P(B) are added, the occasions on which A and B both occur are counted twice. To adjust for this, P(AB) is subtracted. <span>If events A and B are mutually exclusive, the joint probability of A and B is 0. Consequently, the probability that either A or B occurs is simply the sum of the unconditional probabilities of A and B: P (A or B) = P(A) + P(B). What is the probability t

#### Annotation 1645894307084

convoluted

1. adjective (especially of an argument, story, or sentence) extremely complex and difficult to follow. "its convoluted narrative encompasses all manner of digressions"

2. technical intricately folded, twisted, or coiled. "walnuts come in hard and convoluted shells"

 synonyms: complicated , complex , involved , elaborate , serpentine , labyrinthine , tortuous , tangled , Byzantine ; More Rube Goldberg ; confused , confusing , bewildering, baffling "his convoluted answers did nothing to help his credibility"

rySearch help Tools Any time Any time Past hour Past 24 hours Past week Past month Past year Custom range... Customised date range From To All results All results Verbatim About 649,000 results (0.47 seconds) Search Results Dictionary <span>con·vo·lut·ed ˈkänvəˌlo͞odəd/ adjective adjective: convoluted 1 . (especially of an argument, story, or sentence) extremely complex and difficult to follow. "its convoluted narrative encompasses all manner of digressions" synonyms: complicated, complex, involved, elaborate, serpentine, labyrinthine, tortuous, tangled, Byzantine; More Rube Goldberg; confused, confusing, bewildering, baffling "his convoluted answers did nothing to help his credibility" antonyms: straightforward 2 . technical intricately folded, twisted, or coiled. "walnuts come in hard and convoluted shells" Origin late 18th century: past participle of convolute, from Latin convolutus, past participle of convolvere ‘roll together, intertwine’ (see convolve). con·vo·lute ˈkänvəˌlo͞ot/ verb p

#### Annotation 1645897190668

The logic behind the addition rule for probabilities is that when P(A) and P(B) are added, the occasions on which A and B both occur are counted twice. To adjust for this, P(AB) is subtracted.

Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur
e or." In other words, either one event can occur or both events can occur. Such probabilities are calculated using the addition rule for probabilities. P(A or B) = P(A) + P(B) - P(AB) <span>The logic behind this formula is that when P(A) and P(B) are added, the occasions on which A and B both occur are counted twice. To adjust for this, P(AB) is subtracted. If events A and B are mutually exclusive, the joint probability of A and B is 0. Consequently, the probability that either A or B occurs is simply the sum of the unconditio

#### Annotation 1645899549964

Despite the convoluted nature of this method, it has the advantage of being easy to generalize to three or more events. For example, the probability of rolling dice three times and getting a six on at least one of the three rolls is: 1 - 5/6 x 5/6 x 5/6 = 0.421

Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur
is 5/6. Therefore, the probability of getting a number from 1 to 5 on both rolls is: 5/6 x 5/6 = 25/36. This means that the probability of not getting a 1 to 5 on both rolls (getting a 6 on at least one roll) is: 1-25/36 = 11/36. <span>Despite the convoluted nature of this method, it has the advantage of being easy to generalize to three or more events. For example, the probability of rolling dice three times and getting a six on at least one of the three rolls is: 1 - 5/6 x 5/6 x 5/6 = 0.421 <span><body><html>

Article 1645901122828

Subject 4. Multiplication Rule for Independent Events

Two events, A and B, are independent if and only if P(A|B) = P(A), or equivalently, P(B|A) = P(B). That is, the occurrence of one event has no influence on the probability of the occurrence of the other event. In more detail, whether or not B occurs will have no effect on the probability of A and vice versa. Thus, there will be no difference between P(A|B) and P(A), and similarly there will be no difference between P(B|A) and P(B). For example, suppose you flip a coin twice. The event of getting heads on the first flip does not affect the probability of getting heads on the second flip. Therefore, the event of getting heads on the second flip is independent of the event of getting heads on the first flip. When two events are not independent, they must be dependent: the occurrence of one is related to the probability of the occurrence of the other. If we are trying to forecast one event, information about a dependent event will be useful but information about an independent event will no

#### Flashcard 1645902433548

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Question
Two events, A and B, are independent if and only if [...]
P(A|B) = P(A),

or equivalently, P(B|A) = P(B).

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Subject 4. Multiplication Rule for Independent Events
Two events, A and B, are independent if and only if P(A|B) = P(A), or equivalently, P(B|A) = P(B). That is, the occurrence of one event has no influence on the probability of the occurrence of the other event. In more detail, whether or not B occurs will have no effect on

#### Flashcard 1645904792844

Tags
Question
When the occurrence of one event has no influence on the probability of the occurrence of the other event.

Independent events

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Subject 4. Multiplication Rule for Independent Events
Two events, A and B, are independent if and only if P(A|B) = P(A), or equivalently, P(B|A) = P(B). That is, the occurrence of one event has no influence on the probability of the occurrence of the other event. In more detail, whether or not B occurs will have no effect on the probability of A and vice versa. Thus, there will be no difference between P(A|B) and P(A), and similarly

#### Annotation 1645907152140

When two events are not independent, they must be dependent: the occurrence of one is related to the probability of the occurrence of the other.

Subject 4. Multiplication Rule for Independent Events
vent of getting heads on the first flip does not affect the probability of getting heads on the second flip. Therefore, the event of getting heads on the second flip is independent of the event of getting heads on the first flip. <span>When two events are not independent, they must be dependent: the occurrence of one is related to the probability of the occurrence of the other. If we are trying to forecast one event, information about a dependent event will be useful but information about an independent event will not be useful. Examp

#### Flashcard 1645908725004

Tags
Question
[...] : the occurrence of one event is related to the probability of the occurrence of the other.
dependent events

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Subject 4. Multiplication Rule for Independent Events
ffect the probability of getting heads on the second flip. Therefore, the event of getting heads on the second flip is independent of the event of getting heads on the first flip. When two events are not independent, they must be <span>dependent: the occurrence of one is related to the probability of the occurrence of the other. If we are trying to forecast one event, information about a dependent event will be useful but information about an independent event will not be useful. Examp

#### Annotation 1645911084300

If we are trying to forecast one event, information about a dependent event will be useful but information about an independent event will not be useful.

Subject 4. Multiplication Rule for Independent Events
nd flip is independent of the event of getting heads on the first flip. When two events are not independent, they must be dependent: the occurrence of one is related to the probability of the occurrence of the other. <span>If we are trying to forecast one event, information about a dependent event will be useful but information about an independent event will not be useful. Example 1 If C = {the price of insurance share C goes up} and D = {the price of insurance share D goes up}, then clearly C and D are dependent events, because

#### Flashcard 1645912657164

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Question

If A and B are independent, the probability that events A and B both occur is:

P(A and B) = P(A) x P(B)

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Subject 4. Multiplication Rule for Independent Events
hite car}, then events A and B are clearly independent, as the one almost certainly has no bearing upon the other. Remember that if A and B are independent, Ac and Bc will also be independent. A and B are two events. <span>If A and B are independent, the probability that events A and B both occur is: P(A and B) = P(A) x P(B) In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B. This relationship is known as the multiplication

#### Flashcard 1645915016460

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Question
multiplication rule for independent events.
P(A and B) = P(A) x P(B)

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Subject 4. Multiplication Rule for Independent Events
nd B both occur is: P(A and B) = P(A) x P(B) In other words, the probability of A and B both occurring is the product of the probability of A and the probability of B. This relationship is known as the <span>multiplication rule for independent events. What is the probability that a fair coin will come up with heads twice in a row? Two events must occur: heads on the first toss and heads on the second toss. Since the prob

#### Flashcard 1645917375756

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Question

For any number of independent events E1, E2.....En, the probability that all of them occur is:

P(E1 and E2..... and En) = [...]
P(E1) x P(E2) x ..... x P(En)

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Subject 4. Multiplication Rule for Independent Events
in the deck, the probability of the first event is 1/52. Since 13/52 = 1/4 of the deck is composed of clubs, the probability of the second event is 1/4. Therefore, the probability of both events is: 1/52 x 1/4 = 1/208. Similarly, <span>for any number of independent events E 1 , E 2 .....E n , the probability that all of them occur is: P(E 1 and E 2 ..... and E n ) = P(E 1 ) x P(E 2 ) x ..... x P(E n ) Example In a bullish market, three shares, chosen from different sectors of the market, have probabilities of 0.6, 0.5 and 0.8 that their share prices will ris

#### Annotation 1645919735052

Warning: It is important to note that multiplying individual probabilities together can only be done if the events that make up those probabilities are independent. If the events are dependent, this process is not valid.

Subject 4. Multiplication Rule for Independent Events
. If we wish to calculate the probability that all three shares will rise in price on the same day, we can use the results above to get: 0.6 x 0.5 x 0.8 = 0.24 (i.e., the individual probabilities multiplied together) <span>Warning: It is important to note that multiplying individual probabilities together can only be done if the events that make up those probabilities are independent. If the events are dependent, this process is not valid. To calculate the probability that, of the three shares above, none will have a price rise on a particular day, we can multiply the probabilities of the complementary events

#### Annotation 1645922618636

A binomial experiment is a statistical experiment that has the following properties:

• The experiment consists of n repeated trials.
• Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.
• The probability of success, denoted by P, is the same on every trial.
• The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.