Question 1

The expected value of a discrete random variable is the average value for the random variable over many repeats of the experiment.

Accepted Answer

The expected value of a discrete random variable is indeed the average, or mean, value it takes over a large number of trials, representing the long-run average outcome of a random variable.

Question 2

A description of how the probabilities are distributed over the values the random variable can assume is called a random variable.

Accepted Answer

A description of how the probabilities are distributed over the values the random variable can assume is called a probability distribution, not a random variable.

Question 3

One of the conditions for a binomial experiment is that the probability of success on any one trial changes throughout the experiment.

Accepted Answer

One of the conditions for a binomial experiment is that the probability of success on any one trial must remain constant throughout the experiment.

Question 4

The standard deviation of a discrete probability distribution is the positive square root of the variance, which determines the expected value of the distribution.

Accepted Answer

The standard deviation of a discrete probability distribution is indeed the positive square root of the variance, but it measures the spread of the distribution around the mean, not the expected value of the distribution. The expected value (or mean) is a separate measure.

Question 5

The expected value or mean of a Poisson distribution is the same as the variance.

Accepted Answer

In a Poisson distribution, the mean (expected value) and the variance are both equal to λ (lambda), where λ is the rate at which events occur.

Question 6

A probability distribution identifies the probabilities that are assigned to all possible values of a random variable.

Accepted Answer

A probability distribution specifies how probabilities are distributed over the values of a random variable, assigning a probability to each possible value the variable can take.

Question 7

In a binomial experiment x is always less than or equal to n, the number of trials.

Accepted Answer

In a binomial experiment, $x$ represents the number of successes, which cannot exceed $n$, the total number of trials.

Question 8

The first step in producing a probability distribution is to identify values for the random variable.

Accepted Answer

The answer of The first step in producing a probability...

Question 9

The mean of a discrete probability distribution is generally referred to as the expected value of the distribution.

Accepted Answer

The mean of a discrete probability distribution is indeed referred to as the expected value, which is calculated as the sum of each possible value multiplied by its probability of occurrence.

Question 10

The symbol "x" is used to denote the random variable while the symbol "P(x)" is used to denote the probabilities associated with the random variable.

Accepted Answer

The symbol "x" is commonly used to denote a random variable, and "P(x)" is used to denote the probability of the random variable assuming certain values.

Question 11

The binomial probability function is composed of two parts, the first of which computes the probability of each of the ways in which the x successes in n trials can occur.

Accepted Answer

The answer of The binomial probability function is composed of...

Question 12

One of the conditions for a binomial experiment is that the trials are statistically independent.

Accepted Answer

In a binomial experiment, each trial must be independent, meaning the outcome of one trial does not affect the outcome of another.

Question 13

The binomial probability function is composed of two parts, the second of which computes the probability of each of the ways in which the x successes in n trials can occur.

Accepted Answer

The binomial probability function indeed consists of two parts: the first part calculates the number of ways to choose x successes out of n trials (combinatorial part), and the second part computes the probability of each of these combinations occurring, based on the success probability p and the failure probability (1-p).

Question 14

One of the conditions for a Poisson experiment is that the average number of occurrences per unit of time, space, or distance is constant and proportionate to the size of the unit of time, space, or distance involved.

Accepted Answer

In a Poisson experiment, it is indeed a condition that the average rate (mean number of occurrences) per unit of time, space, or distance must be constant across different intervals or regions of the same size, reflecting the requirement for a fixed rate of occurrence for the process being modeled.

Question 15

The number of damaged items found on a shelf in a grocery store when taking inventory is:
A)a discrete random variable
B)a continuous random variable
C)either a continuous or a discrete random variable, depending on the number of the items found
D)either a continuous or a discrete random variable, depending on the type of item
E)a complex random variable

Accepted Answer

The number of damaged items can only take integer values (0, 1, 2, 3, ...), making it a discrete random variable, as it counts occurrences.

Question 16

The number of customers that enter a store during one day is an example of:
A)a continuous random variable
B)a discrete random variable
C)either a continuous or a discrete random variable, depending on the number of the customers
D)either a continuous or a discrete random variable, depending on the gender of the customers
E)none of the above

Accepted Answer

The number of customers that enter a store during one day is a discrete random variable because it can only take on integer values (i.e. you can't have 3.5 customers).

Question 17

The expected value of a discrete random variable is the value of the random variable that occurs most frequently.

Accepted Answer

The expected value of a discrete random variable is the weighted average of all possible values that this random variable can take on, where the weights are the probabilities of each outcome, not the most frequently occurring value.

Question 18

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy.The random variable is the number of sales made.This random variable is a:
A)a discrete random variable
B)a continuous random variable
C)either a continuous or a discrete random variable, depending on the number of the calls made
D)either a continuous or a discrete random variable, depending on the gender of the customers
E)a complex random variable

Accepted Answer

The number of sales made from telephone calls can only take on integer values (0, 1, 2, ..., 80), making it a discrete random variable. Continuous random variables, in contrast, can take on any value within a range, which does not apply in this scenario.

Question 19

When playing a round of golf, the number of pars is considered to be a discrete variable.

Accepted Answer

In golf, the number of pars refers to the count of holes completed in the prescribed number of strokes, which is a countable quantity, making it a discrete variable.

Question 20

When playing a round of golf, the distance of the drive off the second tee in feet is considered to be a discrete variable.

Accepted Answer

The distance of the drive off the second tee in feet is a continuous variable because it can take on any value within a range, including fractions, rather than being limited to distinct, separate values.

Quiz 5: Discrete Probability Distributions