Question 1

For a discrete probability distribution,the value of p(x)for each value of x falls between -1 and 1.

Accepted Answer

The probability of each value in a discrete probability distribution falls between 0 and 1, inclusive. It cannot be negative or greater than 1.

Question 2

The mean and the variance of a Poisson random variable are equal.

Accepted Answer

This statement is true. The mean and variance of a Poisson random variable are both equal to λ, the parameter of the Poisson distribution.

Question 3

If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.

Accepted Answer

This example is a description of a hypergeometric distribution.

Question 4

A correlation coefficient is a unitless measure of the linear relationship between two random variables.

Accepted Answer

A correlation coefficient measures the strength and direction of the linear relationship between two random variables, and it is unitless, meaning it does not have a physical unit or measurement.

Question 5

The expected value of the discrete random variable x is the population mean.

Accepted Answer

This statement is true. The expected value of a random variable x is defined as the weighted average of all the possible outcomes of x, with the weights being the probabilities of each outcome. The population mean is also defined as the average value of the entire population, which can also be found using the formula for expected value. Therefore, the expected value of x is equal to the population mean.

Question 6

In a hypergeometric probability distribution of a population of N items,r refers to the number of successes and N - r to the number of failures.

Accepted Answer

This is correct. In a hypergeometric distribution, r represents the number of successes and N-r represents the number of failures.

Question 7

With two random variables x and y,a positive covariance says that as x increases,y tends to increase in a linear fashion.

Accepted Answer

A positive covariance indicates that as one variable increases, the other tends to increase as well. However, it doesn't necessarily imply a linear relationship between the two variables.

Question 8

A discrete random variable may assume a countable number of outcome values.

Accepted Answer

A discrete random variable can only take on a countable number of values, such as 0, 1, 2, 3, ... or -1, 0, 1, 2, 3, ... This is in contrast to a continuous random variable which can take on any value within a certain range.

Question 9

If the population size is at least 20 times larger than the sample size,a hypergeometric distribution can be approximated by the binomial distribution.

Accepted Answer

This is true because as the population size becomes significantly larger than the sample size, the probability of selecting an individual from the population becomes close to constant, making it similar to the assumptions of the binomial distribution.

Question 10

In a binomial distribution,the random variable X is continuous.

Accepted Answer

In a binomial distribution, the random variable X is discrete, not continuous. It represents the number of successes in a fixed number of trials with a constant probability of success.

Question 11

The binomial experiment consists of n independent,identical trials,each of which results in either success or failure and is such that the probability of success on any trial is the same.

Accepted Answer

This is the definition of a binomial experiment.

Question 12

Depending on the mean of the Poisson distribution,the distribution can either be very skewed to the right or quite symmetrical.

Accepted Answer

The answer of Depending on the mean of the Poisson...

Question 13

The mean of the binomial distribution is np(1 - p).

Accepted Answer

The answer of The mean of the binomial distribution is...

Question 14

In a binomial experiment,the results of one trial are dependent on the results of other trials.

Accepted Answer

In a binomial experiment, each trial is independent of the results of other trials.

Question 15

The internal auditor for your company believes that 10 percent of their invoices contain errors.To check this theory,20 invoices are randomly selected and 5 are found to have errors.The claim of the auditor will be rejected.

Accepted Answer

The answer of The internal auditor for your company believes...

Question 16

The standard deviation of a discrete random variable measures the spread of the population of all possible values of x.

Accepted Answer

The standard deviation is a measure of the variability or spread of a distribution, including for discrete random variables.

Question 17

The hypergeometric probability distribution can be approximated by the Poisson distribution.

Accepted Answer

The hypergeometric distribution is approximated by a binomial distribution.

Question 18

A Poisson random variable is a continuous variable that can be used to describe the number of occurrences of an event over a specified interval of time or space.

Accepted Answer

A Poisson random variable is a discrete variable, not a continuous one.

Question 19

The variable Home Ownership can take on one of two values,1 if the person living in a home owns the home and zero if the person living in a home does not own the home.This is an example of a discrete random variable.

Accepted Answer

Since the variable Home Ownership can only take on two specific values, it is a discrete random variable.

Question 20

The time (in seconds)it takes for an athlete to run 50 meters is an example of a continuous random variable.

Accepted Answer

A continuous random variable is a variable that can take on any value within a certain range, such as time or distance. In this case, the time it takes for an athlete to run 50 meters can take on any value within a continuous range of time, making it a continuous random variable.

Quiz 5: Discrete Random Variables