Question 1

A continuous random variable may assume
A)any value in an interval or collection of intervals
B)only integer values in an interval or collection of intervals
C)only fractional values in an interval or collection of intervals
D)only the positive integer values in an interval

Accepted Answer

A continuous random variable can take any value within a range or collection of ranges, meaning that it can take on both integer and non-integer values.

Question 2

The weight of an object, measured to the nearest gram, 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 weight of the object
D)either a continuous or a discrete random variable depending on the units of measurement

Accepted Answer

Since the weight of an object can only be measured in whole grams (not fractions of grams), it is a discrete random variable.

Question 3

A random variable that can assume only a finite number of values is referred to as a(n)
A)infinite sequence
B)finite sequence
C)discrete random variable
D)discrete probability function

Accepted Answer

A discrete random variable is one that can only take on a finite or countable number of values. Therefore, option C is the best choice. Option A is incorrect because an infinite sequence can have an infinite number of values. Option B is incorrect because it implies that the sequence has an end point, which may not be the case. Option D is incorrect because a discrete probability function is a function that assigns probabilities to all possible outcomes of a discrete random variable.

Question 4

Which of the following is(are) required condition(s) for a discrete probability function?
A)$\Sigma$f(x) $\ge$ 
B)f(x)$\ge$  1 for all values of x
C)f(x) $\lt$ 0
D)None of the answers is correct.

Accepted Answer

The answer of Which of the following is(are) required condition(s)...

Question 5

Excel's __________ function can be used to compute the expected value of a discrete random variable.
A)SUMPRODUCT
B)AVERAGE
C)MEDIAN
D)VAR

Accepted Answer

The SUMPRODUCT function in Excel can be used to compute the expected value of a discrete random variable by multiplying each possible value of the variable by its corresponding probability and then summing all these products.

Question 6

Which of the following statements about a discrete random variable and its probability distribution are true?
A)Values of the random variable can never be negative.
B)Negative values of f(x) are allowed as long as $\Sigma$f(x) = 1.
C)Values of f(x) must be greater than or equal to zero.
D)The values of f(x) increase to a maximum point and then decrease.

Accepted Answer

Option A is not necessarily true as some discrete random variables can take negative values. Option B is incorrect because negative values of probability density function could not be possible. Option D is also incorrect because a probability distribution should have non-negative probabilities so the value of f(x) must be greater than or equal to zero. Therefore, option C is the only true statement among the given options.

Question 7

A measure of the average value of a random variable is called a(n)
A)variance
B)standard deviation
C)expected value
D)None of the answers is correct.

Accepted Answer

The expected value is defined as the average value of a random variable over a large number of trials. It is a measure of central tendency and represents the long-run expected value of the variable. The variance and standard deviation are measures of dispersion around the expected value, not the average value itself.

Question 8

The expected value of a discrete random variable
A)is the most likely or highest probability value for the random variable
B)will always be one of the values x can take on, although it may not be the highest probability value for the random variable
C)is the average value for the random variable over many repeats of the experiment
D)All of the answers are correct.

Accepted Answer

The expected value of a discrete random variable is calculated by taking the weighted average of all possible values that the random variable can take on, where the weights are the probabilities of each value occurring. It represents the expected value over many repeats of the experiment. It may not be the most likely or highest probability value for the random variable, and it may not be one of the values x can take on. Therefore, the correct choice is C.

Question 9

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a
A)discrete random variable
B)continuous random variable
C)complex random variable
D)None of the answers is correct.

Accepted Answer

The speed of automobiles on a highway can take on any value within a range, making it a continuous random variable.

Question 10

Variance is
A)a measure of the average, or central value of a random variable
B)a measure of the dispersion of a random variable
C)the square root of the standard deviation
D)the sum of the deviation of data elements from the mean

Accepted Answer

Variance is a statistical measure for how much the observations in a data set are spread out. It quantifies the amount of variation or dispersion of a set of data values. Option A describes the mean, not the variance. Option C describes the standard deviation, not the variance. Option D describes the sum of deviations, which is not equivalent to the variance.

Question 11

The variance is a weighted average of the
A)square root of the deviations from the mean
B)square root of the deviations from the median
C)squared deviations from the median
D)squared deviations from the mean

Accepted Answer

The variance is calculated by finding the sum of the squared deviations from the mean, divided by the number of data points minus 1. Therefore, the best choice is option D, squared deviations from the mean.

Question 12

Which of the following is not a required condition for a discrete probability function?
A)f(x) $\ge$0 for all values of x
B)$\Sigma$f(x) =  1
C)$\Sigma$f(x) = 0
D)All of the answers are correct.

Accepted Answer

Option C states that the sum of all f(x) values must be equal to 0, which is not a required condition for a discrete probability function. The sum of all f(x) values must be equal to 1, as stated in option B. Option A states that f(x) must be greater than or equal to 0 for all values of x, which is a required condition. Therefore, the correct answer is C.

Question 13

A weighted average of the value of a random variable, where the probability function provides weights is known as
A)a probability function
B)a random variable
C)the expected value
D)None of the answers is correct

Accepted Answer

The weighted average of a random variable with weights provided by the probability function is known as the expected value.

Question 14

The weight of an object, measured in grams, 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 weight of the object
D)either a continuous or a discrete random variable depending on the units of measurement

Accepted Answer

The weight of an object can have any value between two given values, making it a continuous random variable. Additionally, measurement in grams does not limit the number of possible values.

Question 15

A numerical description of the outcome of an experiment is called a
A)descriptive statistic
B)probability function
C)variance
D)random variable

Accepted Answer

A random variable is a variable whose possible values are numerical outcomes of a random phenomenon. It is a way to assign numbers to outcomes of an experiment, thus providing a numerical description of those outcomes.

Question 16

A description of how the probabilities are distributed over the values the random variable can assume is called a
A)probability distribution
B)probability function
C)random variable
D)expected value

Accepted Answer

A probability distribution describes how the probabilities are distributed over the values a random variable can assume. This can be expressed in the form of a probability function or probability density function, depending on whether the variable is discrete or continuous. The expected value is a measure of the central tendency of a probability distribution, but it is not the same as the distribution itself.

Question 17

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is the number of sales made. This random variable is a
A)discrete random variable
B)continuous random variable
C)complex random variable
D)None of the answers is correct.

Accepted Answer

The random variable (number of sales made) can only take on discrete values (0, 1, 2, 3, ..., 80) and not any value in between, making it a discrete random variable.

Question 18

Excel's __________ function can be used to compute the variance of a discrete random variable.
A)SUMPRODUCT
B)AVERAGE
C)MEDIAN
D)VAR

Accepted Answer

SUMPRODUCT function can be used to compute the variance of a discrete random variable by multiplying each value by its corresponding probability and then summing up these products.

Question 19

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

Accepted Answer

The number of customers that enter a store is a discrete random variable because it can only take on whole, countable values (e.g. 0, 1, 2, 3...). It is not a continuous random variable because it cannot take on all values within a certain range.

Question 20

The expected value of a random variable is the
A)value of the random variable that should be observed on the next repeat of the experiment
B)value of the random variable that occurs most frequently
C)square root of the variance
D)None of the answers is correct.

Accepted Answer

The expected value of a random variable is a theoretical mean of all possible outcomes, weighted by their probabilities, not necessarily any of the options given. It is not specifically the value observed next, the most frequent value, or the square root of the variance.

Quiz 5: Discrete Probability Distributions

A continuous random variable may assume

The weight of an object, measured to the nearest gram, is an example of

A random variable that can assume only a finite number of values is referred to as a(n)

Which of the following is(are) required condition(s) for a discrete probability function?

Excel's __________ function can be used to compute the expected value of a discrete random variable.

Which of the following statements about a discrete random variable and its probability distribution are true?

A measure of the average value of a random variable is called a(n)

The expected value of a discrete random variable

An experiment consists of measuring the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a

Variance is

The variance is a weighted average of the

Which of the following is not a required condition for a discrete probability function?

A weighted average of the value of a random variable, where the probability function provides weights is known as

The weight of an object, measured in grams, is an example of

A numerical description of the outcome of an experiment is called a

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

An experiment consists of making 80 telephone calls in order to sell a particular insurance policy. The random variable in this experiment is the number of sales made. This random variable is a

Excel's __________ function can be used to compute the variance of a discrete random variable.

The number of customers that enter a store during one day is an example of

The expected value of a random variable is the