Deck 5: Discrete Probability Distributions

Question 1

A risk-loving consumer will take on risk even if the expected gain is negative.

Answer 1

True

Question 2

The expected value of a random variable X can be referred to as the population mean.

Answer 2

True

Question 3

A discrete random variable X may assume an (infinitely) uncountable number of distinct values.

Answer 3

False

Question 4

A probability distribution of a continuous random variable X gives the probability that X takes on a particular value x, P(X = x).

Question 5

The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance.

Question 6

A risk-averse consumer ignores risk and makes his or her decisions solely on the basis of expected value.

Question 7

A binomial random variable is defined as the number of successes achieved in n trials of a Bernoulli process.

Question 8

A cumulative probability distribution of a random variable X is the probability P(X = x), where X is equal to a particular value x.

Question 9

We use the hypergeometric distribution in place of the binomial distribution when we are sampling with replacement from a population whose size N is significantly larger than the sample size n.

Question 10

Given two random variables X and Y, the expected value of their sum, E (X + Y), is equal to the sum of their individual expected values, E (X) and E (Y).

Question 11

A random variable is a function that assigns numerical values to the outcomes of a random experiment.

Question 12

A Bernoulli process consists of a series of n independent and identical trials of an experiment such that in each trial there are three possible outcomes and the probabilities of each outcome remain the same.

Question 13

A risk-neutral consumer ignores risk and makes his or her decisions solely on the basis of expected value.

Question 14

The ounces of soda consumed by an adult next month are an example of a discrete random variable.

Question 15

A Poisson random variable counts the number of successes (occurrences of a certain event) over a given interval of time or space.

Question 16

Testing whether the computer is infected or not would be best described using binomial probability distribution.

Question 17

The variance of a random variable X provides us with a measure of central location of the distribution of X.

Question 18

A risk-averse consumer may decline a risky prospect even if it offers a positive expected value.

Question 19

The expected value of simple information is the mean of a discrete probability distribution when the discrete random variable is expressed in term of dollars.

Question 20

A continuous random variable X assumes an (infinitely) uncountable number of distinct values.

Question 21

What is a characteristic of the mass function of a discrete random variable X?

A) The sum of probabilities P(X = x) over all possible values x is 1.
B) For every possible value x, the probability P(X = x) is between 0 and 1.
C) Describes all possible values x with the associated probabilities P(X = x).
D) All of the above.

Question 22

Consider the following cumulative distribution function for the discrete random variable X. What is the probability that X is less than or equal to 2?

A) 0.14
B) 0.30
C) 0.44
D) 0.56

Question 23

Which of the following can be represented by a discrete random variable?

A) The number of obtained spots when rolling a six-sided die
B) The height of college students
C) The average outside temperature taken every day for two weeks
D) The finishing time of participants in a cross-country meet

Question 24

Consider the following discrete probability distribution. What is the probability that X is greater than 0?

A) 0.10
B) 0.35
C) 0.55
D) 0.65

Question 25

Consider the following discrete probability distribution. What is the probability that X is 0?

A) 0.10
B) 0.35
C) 0.55
D) 0.65

Question 26

Consider the following discrete probability distribution. What is the probability that X is less than 5?

A) 0.10
B) 0.15
C) 0.35
D) 0.45

Question 27

To illustrate the possible outcomes and their associated probabilities we can construct a probability ________.

Question 28

Which of the following can be represented by a discrete random variable?

A) The circumference of a randomly generated circle
B) The time of a flight between Chicago and New York
C) The number of defective light bulbs in a sample of five
D) The average distance achieved in a series of long jumps

Question 29

An Excel's function ________ is used for calculating Poisson probabilities.

Question 30

The following formula defines the ________ of a hypergeometric random variable
n .

Question 31

A risk-averse consumer demands a(n) ________ expected gain as compensation for taking risk.

Question 32

Consider the following discrete probability distribution. What is the probability that X is negative?

A) 0.00
B) 0.10
C) 0.15
D) 0.35

Question 33

Which of the following can be represented by a continuous random variable?

A) The time of a flight between Chicago and New York
B) The number of defective light bulbs in a sample of five
C) The number of arrivals to a drive-through bank window in a four-hour period
D) The score of a randomly selected student on a five-question multiple-choice quiz

Question 34

Which of the following can be represented by a continuous random variable?

A) The average temperature in Tampa, Florida, during the month of July
B) The number of typos found on a randomly selected page of this test bank
C) The number of students who will get financial assistance in a group of 50 randomly selected students
D) The number of customers who visit a department store between 10:00 a.m. and 11:00 a.m. on Mondays

Question 35

The hypergeometric probability distribution is appropriate in applications where we cannot assume the trials are ________.

Question 36

The Excel's function HYPERGEOM.DIST can be used to solve hypergeometric probabilities.

Question 37

What are the two key properties of a discrete probability distribution?

A) 0 ≤ P(X = x) ≤1 and ∑P(X = x_i ) = 0
B) 0 ≤ P(X = x) ≤1 and ∑P(X = x_i ) = 1
C) -1 ≤ P(X = x) ≤1 and ∑P(X = x_i ) = 1
D) -1 ≤ P(X = x) ≤1 and ∑P(X = x_i ) = 0

Question 38

The equation used to calculate binomial probabilities relies on permutations of n objects selected x at a time.

Question 39

The number of syntactic errors found in a program code would best be described using a Poisson probability distribution.

Question 40

The risk of the portfolio depends not only on the individual risks of the assets but also on the ________ between the asset returns.

Question 41

Consider the following probability distribution. The standard deviation is ________.

A) 1.14
B) 1.29
C) 1.65
D) 1.94

Question 42

The number of homes sold by a realtor during a month has the following probability distribution: What is the expected number of homes sold by the realtor during a month?

A) 1
B) 1.2
C) 1.5
D) 2

Question 43

The number of homes sold by a realtor during a month has the following probability distribution: What is the probability that the realtor sells no more than one house during a month?

A) 0.20
B) 0.40
C) 0.60
D) 0.80

Question 44

Consider the following probability distribution. The standard deviation is ________.

A) 0.89
B) 0.94
C) 1.65
D) 1.90

Question 45

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the probability that the salesperson sells no more than one car during a week?

A) 0.20
B) 0.40
C) 0.60
D) 0.80

Question 46

An analyst has constructed the following probability distribution for firm X's predicted return for the upcoming year. The expected value and the variance of this distribution are ________ and ________.

A) Option A
B) Option B
C) Option C
D) Option D

Question 47

The number of homes sold by a realtor during a month has the following probability distribution: What is the probability that the realtor will sell at least one house during a month?

A) 0.20
B) 0.40
C) 0.60
D) 0.80

Question 48

Consider the following cumulative distribution function for the discrete random variable X. What is the probability that X is greater than 2?

A) 0.14
B) 0.30
C) 0.44
D) 0.56

Question 49

An analyst estimates that the year-end price of a stock has the following probabilities: The stock's expected price at the end of the year is ________.

A) $87.50
B) $88.50
C) $89.00
D) $90.00

Question 50

Consider the following probability distribution. The variance is ________.

A) 0.89
B) 0.94
C) 1.65
D) 1.90

Question 51

Consider the following probability distribution. The expected value is ________.

A) -1.0
B) -0.1
C) 0.1
D) 1.0

Question 52

An analyst believes that a stock's return depends on the state of the economy, for which she has estimated the following probabilities: According to the analyst's estimates, the expected return of the stock is ________.

A) 7.8%
B) 11.4%
C) 11.7%
D) 13.0%

Question 53

We can think of the expected value of a random variable X as ________.

A) the long-run average of the random variable values generated over 100 independent repetitions
B) the long-run average of the random variable values generated over 1,000 independent repetitions
C) the long-run average of the random variable values generated over infinitely many independent repetitions
D) the long-run average of the random variable values generated over a finite number of independent repetitions

Question 54

Consider the following probability distribution. The variance is ________.

A) 1.14
B) 1.29
C) 1.65
D) 1.94

Question 55

Consider the following cumulative distribution function for the discrete random variable X. What is the probability that X equals 2?

A) 0.14
B) 0.30
C) 0.44
D) 0.56

Question 56

The number of homes sold by a realtor during a month has the following probability distribution: What is the standard deviation of the number of homes sold by the realtor during a month?

A) 0.56
B) 0.75
C) 1
D) 1.2

Question 57

The expected value of a random variable X can be referred to or denoted as ________.

A) µ
B) E(X)
C) The population mean
D) All of the above

Question 58

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the expected number of cars sold by the salesperson during a week?

A) 0
B) 0.8
C) 1
D) 1.5

Question 59

Consider the following probability distribution. The expected value is ________.

A) 0.9
B) 1.5
C) 1.9
D) 2.5

Question 60

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the probability that the salesperson will sell one car during a week?

A) 0.20
B) 0.40
C) 0.60
D) 0.80

Question 61

An investor has a $100,000 portfolio of which $75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The standard deviation of the portfolio is ________.

A) 9.39 (%)
B) 14.19 (%).
C) 88.23 (%)².
D) 201.41 (%)².

Question 62

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective?

A) 0.00729
B) 0.0081
C) 0.081
D) 0.03

Question 63

A consumer who is risk averse is best characterized as ________.

A) a consumer who may accept a risky prospect even if the expected gain is negative
B) a consumer who demands a positive expected gain as compensation for taking risk
C) a consumer who completely ignores risk and makes his or her decisions based solely on expected values
D) None of the above

Question 64

An investor has a $100,000 portfolio of which $75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The expected return of the portfolio is ________.

A) 6.30%
B) 6.75%
C) 7.38%
D) 13.50%

Question 65

A consumer who is risk neutral is best characterized as ________.

A) a consumer who may accept a risky prospect even if the expected gain is negative
B) a consumer who demands a positive expected gain as compensation for taking risk
C) a consumer who completely ignores risk and makes his or her decisions based solely on expected values
D) None of the above

Question 66

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that no more than one in a random sample of four calculators is defective?

A) 0.2916
B) 0.3439
C) 0.6561
D) 0.9477

Question 67

An investor has a $200,000 portfolio of which $120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The expected return of the portfolio is ________.

A) 2.60%
B) 5.04%
C) 7.64%
D) 14.90%

Question 68

How would you characterize a consumer who is risk loving?

A) A consumer who may accept a risky prospect even if the expected gain is negative.
B) A consumer who demands a positive expected gain as compensation for taking risk.
C) A consumer who completely ignores risk and makes his or her decisions solely on the basis of expected values.
D) None of the above.

Question 69

Given the information in the accompanying table, calculate the correlation coefficient between the returns on Stocks A and B.

A) -0.212
B) -0.167
C) 0.167
D) 0.212

Question 70

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that at least one in a random sample of four calculators is defective?

A) 0.0010
B) 0.2916
C) 0.3439
D) 0.6561

Question 71

Which of the following statements is the most accurate about a binomial random variable?

A) It has a bell-shaped distribution.
B) It is a continuous random variable.
C) It counts the number of successes in a given number of trials.
D) It counts the number of successes in a specified time interval or region.

Question 72

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: What is the standard deviation of the number of cars sold by the salesperson during a week?

A) 0.56
B) 0.75
C) 0.80
D) 1

Question 73

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that at least one of them has a degree in economics?

A) 0.300
B) 0.343
C) 0.657
D) 0.900

Question 74

An investor has a $200,000 portfolio of which $120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The portfolio variance is ________.

A) 8.17%
B) 13.80%
C) 66.78 (%)^2
D) 190.70 (%)²

Question 75

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that at most 3 of the light bulbs will be defective?

A) 0.0105
B) 0.0115
C) 0.9885
D) 0.9990

Question 76

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that none of them has a degree in economics?

A) 0.027
B) 0.300
C) 0.343
D) 0.900

Question 77

An investor has a $200,000 portfolio of which $120,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The correlation coefficient between the returns on Stocks A and B is ________.

A) -0.17
B) 0.20
C) 0.80
D) 4.97

Question 78

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that none of the light bulbs will be defective?

A) 0.0105
B) 0.0746
C) 0.3151
D) 0.5987

Question 79

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that two light bulbs will be defective?

A) 0.0105
B) 0.0746
C) 0.3151
D) 0.5987

Question 80

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?

A) 0.0010
B) 0.2916
C) 0.3439
D) 0.6561