Question 1

Which of the following is the best example of a discrete random variable?

Accepted Answer

The number of cars passing through a toll booth in an hour

Question 2

A random variable $$x$$ represents the number of heads in 10 coin tosses. Which statement is true?

Accepted Answer

$$x is a $$discrete random variable because the number of heads can only be whole numbers between 0 and 10.

Question 3

Which of the following distributions is NOT a valid probability distribution?

Accepted Answer

$$x: 1, 2, 3, 4$$;\ P(x): 0.5, 0.3, 0.1, 0.2$

Question 4

Suppose a probability distribution is given by $$x: 0, 1, 2, 3$$ and $$P(x): 0.1, 0.3, 0.4, 0.2. $$What is the mean (expected value) of $$x$$?

Accepted Answer

$$1.7$$

Question 5

A company tracks the number of defective products found in a day: $$x = 0, 1, 2, 3$$ with $$P(x) = 0.5, 0.3, 0.15, 0.05. $$What is the variance of $$x$$?

Accepted Answer

$$0.61$$

Question 6

Which of the following statements about probability distributions is FALSE?

Accepted Answer

The sum of all probabilities in a discrete probability distribution must be less than or equal to 1.

Question 7

A survey finds the probability that a randomly selected person has 0, 1, or 2 credit cards is $$0.22$$, $$0.20$$, and $$0.19$$ respectively. What is the probability that a person has either 1 or 2 credit cards?

Accepted Answer

$$0.39$$

Question 8

Given the probability distribution: $$x: 1, 2, 3, 4, 5$$; $$P(x): 0.16, 0.22, 0.28, 0.20, 0.14$$, what is the standard deviation? (Mean $$\mu = 2.94)$$

Accepted Answer

$$1.27$$

Question 9

A random variable $$x$$ represents the volume of gasoline in a 21-gallon tank. Which statement is correct?

Accepted Answer

$$x is a $$continuous random variable because it can take any value between 0 and 21.

Question 10

In a raffle, 1000 tickets are sold at $$3 each for two prizes: 1000 $$and $500. If you buy one ticket, what is your expected gain?

Accepted Answer

$$-2.50$$

Question 11

Which formula correctly represents the mean $$\mu of a $$discrete random variable $$x$$ with probability distribution $$P(x)$$?

Accepted Answer

$$\mu = \sum x \cdot P(x)$$

Question 12

A discrete probability distribution is given by $$x: 2, 4, 6$$ and $$P(x): 0.3, 0.5, 0.2. $$What is the expected value of $$x$$?

Accepted Answer

$$3.8$$

Question 13

Which of the following is NOT a requirement for a discrete probability distribution?

Accepted Answer

Each probability must be greater than 0.

Question 14

A game costs $$5 to $$play. You have a $$1/100$$ chance to win $$100$$, and a $$99/100$$ chance to win nothing. What is your expected value?

Accepted Answer

$$-4.00$$

Question 15

If the variance of a discrete random variable $$x is$$ $$\$$sigma^2$$ = 2.25$$, what is the standard deviation?

Accepted Answer

$$1.5$$

Question 16

Which of the following best describes the expected value in a profit-and-loss analysis?

Accepted Answer

It represents the average gain or loss per trial over many repetitions.

Question 17

A probability distribution has $$P(x) = -0.1$$ for some $$x. $$What does this indicate?

Accepted Answer

The distribution is not a valid probability distribution.

Question 18

A discrete random variable $$x$$ has the following probability distribution: $$x: 0, 1, 2$$; $$P(x): 0.3, 0.4, 0.3. $$What is the probability that $$x is at $$least 1?

Accepted Answer

$$0.7$$

Question 19

Which formula gives the variance $$\$$sigma^2$$ of a discrete random variable x$ with mean $$\mu$$?

Accepted Answer

$$\$$sigma^2$$ = \sum (x - \mu)^2$ P(x)$$

Question 20

A lottery sells 2000 tickets at $$5 each for prizes of 2000$$, $$1000, 500$$, $$250, and 100. If $$you buy one ticket, what is your expected value? (Assume only one of each prize.)

Accepted Answer

$$-2.05$$

Discrete Probability Distributions: Random Variables, Probability Distributions, and Their Properties

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