Question 1

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 2

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 on any value in an interval or collection of intervals, as opposed to a discrete random variable which can only take on specific, isolated values.

Question 3

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

The weight of an object, when measured to the nearest gram, is counted in whole numbers (1 gram, 2 grams, etc.), making it a discrete random variable because it can only take on specific, separate values. Continuous variables, in contrast, can take on any value within a range.

Question 4

Which of the following is NOT a required condition for a discrete probability function?
A) f(x) ≥ 0 for all values of x
B) ∑f(x) = 1
C) ∑f(x) = 0
D) All of the answers are correct.

Accepted Answer

A discrete probability function must always have non-negative probabilities, so A is required. The sum of all probabilities must equal 1, so B is required. However, the sum of probabilities cannot equal 0, as that would mean there is no chance of any event occurring, making the function invalid. Therefore, C is not a required condition for a discrete probability function.

Question 5

Which of the following statements about a discrete random variable and its probability distribution is true?
A) Values of the random variable can never be negative.
B) Negative values of f(x) are allowed if ∑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

The values of f(x) must be greater than or equal to zero since probabilities cannot be negative. Choice A is incorrect because some discrete random variables, such as stock prices, can take on negative values. Choice B is incorrect because probabilities cannot be negative. Choice D is incorrect because there is no requirement for the values of f(x) to increase to a maximum and then decrease.

Question 6

Highway patrol officers measure the speed of automobiles on a highway using 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

Speed, measured in miles per hour, is a continuous random variable since it can take on any value within a range (e.g. any number between 0 and infinity).

Question 7

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

A continuous random variable can take any value within a given range, and measurements of weight can be infinitely divisible (e.g. an object can weigh 25.1234 grams). Therefore, weight measured in grams is an example of a continuous random variable.

Question 8

The number of customers who 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 is a discrete random variable because it can only take on whole number values (e.g. 0, 1, 2, 3...). It cannot take on fractional or continuous values. The fact that it is one day doesn't affect whether it's continuous or discrete, only the nature of the quantity being measured. The gender of the customers is irrelevant to whether it's continuous or discrete.

Question 9

A marketing manager instructs his team to make 80 telephone calls to attempt to sell an 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 in this experiment is the number of sales made, which is a countable and finite number. Therefore, it is a discrete random variable.

Question 10

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 computed by taking the average of the squared deviations from the mean. Therefore, the correct choice is D, squared deviations from the mean.

Question 11

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 a random variable that can assume only a finite number of values. Option A and B talk about sequences, but not specifically about random variables, and D refers to the function that maps each possible value of a random variable to its probability, but does not define the variable itself.

Question 12

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 numerical description of the outcome of an experiment. It can take different values depending on the outcome of the experiment, which is why it's termed "random."

Question 13

Which of the following is(are) required condition(s) for a discrete probability function?
A) ∑f(x) = 0
B) f(x) ≥ 1 for all values of x
C) f(x) < 0
D) None of the answers is correct.

Accepted Answer

A discrete probability function must satisfy two conditions:

1. The sum of all the probabilities must be equal to 1. This is expressed as ∑f(x) = 1, not ∑f(x) = 0 (option A).

2. The probabilities must be non-negative, meaning f(x) ≥ 0 for all values of x. Option B is incorrect because it suggests that f(x) must be greater than or equal to 1, which is not true. Option C is also incorrect because f(x) cannot be negative.

Therefore, the correct answer is D, none of the answers provided are correct.

Question 14

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 15

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

Accepted Answer

A probability distribution is a description of how probabilities are distributed over the values a random variable can take on. A probability function and random variable are both components of a probability distribution, but they do not fully describe the distribution. The expected value is a measure of the central tendency of a probability distribution, but it is not the same as a description of how probabilities are distributed over values.

Question 16

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 measure of how spread out a set of data is. It measures the average deviation of a set of data points from their mean. Therefore, option B - "a measure of the dispersion of a random variable" - is the correct choice. Options A, C, and D are incorrect as they either refer to other statistical measures or describe properties of variance inaccurately.

Question 17

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 18

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.

Question 19

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 the average value for the random variable over many repeats of the experiment. It is not necessarily the most likely or highest probability value for the random variable, and it may not always be one of the values x can take on. Therefore, options A and B are incorrect. Option D is incorrect as not all of the options are correct.

Question 20

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 a measure of the central tendency of a random variable and represents the average outcome if the same experiment is repeated many times. The variance and standard deviation, on the other hand, measure the spread or dispersion of the random variable around its expected value. None of the answers is not correct because they all have specific meanings and applications in statistics.

Quiz 5: Discrete Probability Distributions

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

A continuous random variable may assume _____.

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

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

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

Highway patrol officers measure the speed of automobiles on a highway using radar equipment. The random variable in this experiment is speed, measured in miles per hour. This random variable is a _____.

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

The number of customers who enter a store during one day is an example of _____.

A marketing manager instructs his team to make 80 telephone calls to attempt to sell an insurance policy. The random variable in this experiment is the number of sales made. This random variable is a _____.

The variance is a weighted average of the _____.

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

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

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

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

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

Variance is _____.

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

The expected value of a random variable is the _____.

The expected value of a discrete random variable _____.

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