Question 1

Which of the following is a discrete random variable?

Accepted Answer

The number of heads obtained when flipping a coin three times.

Question 2

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

Accepted Answer

The random variable must take on only integer values.

Question 3

Suppose $$X is a $$discrete random variable with the following probability distribution: $$P(X=0)=0.2$$, $$P(X=1)=0.5$$, $$P(X=2)=0.3. $$What is $$P(X \leq 1)$$?

Accepted Answer

$$0.7$$

Question 4

Which formula correctly represents the mean (expected value) $$\mu of a $$discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$P(x_i)$$?

Accepted Answer

$$\mu = \sum x_i P(x_i)$$

Question 5

A basketball player shoots three free throws. Let $$X be $$the number of successful shots. Which of the following best describes the probability $$P(X=2)=0.31$$?

Accepted Answer

The probability that the player makes exactly 2 successful shots is 0.31.

Question 6

Which of the following graphs is most appropriate for displaying a discrete probability distribution?

Accepted Answer

A bar graph with gaps between the bars.

Question 7

Suppose a discrete random variable $$X$$ has the following probability distribution: $$x: 0, 1, 2, 3$$; $$P(x): 0.2, 0.4, 0.3, 0.1. $$What is the mean of $$X$$?

Accepted Answer

$$1.3$$

Question 8

If the number of repetitions of an experiment increases, what happens to the difference between the sample mean and the mean of the probability distribution?

Accepted Answer

The difference tends to decrease.

Question 9

Which of the following best describes the expected value of a discrete random variable in a real-world context?

Accepted Answer

It is the long-run average value of the random variable over many repetitions.

Question 10

Which formula is used to compute the standard deviation $$\sigma of a $$discrete random variable $$X$$ with mean $$\mu$$?

Accepted Answer

$$\sigma = \sqrt{\sum (x_i - \mu)^2$ P(x_i)}$$

Question 11

A life insurance policy pays $$\100$$,000$$ if the insured person dies within one year. The probability of death is 0.001$. What is the expected payout for the insurance company?

Accepted Answer

$$\100$

Question 12

Which of the following statements about discrete probability distributions is FALSE?

Accepted Answer

The probabilities can be negative as long as they sum to 1.

Question 13

Suppose you roll a fair six-sided die. Let $$X be $$the number that appears. What is the probability distribution of $$X$$?

Accepted Answer

Each value from 1 to 6 has probability $$\frac{1}{6}.$$

Question 14

Which of the following is an example of a continuous random variable?

Accepted Answer

The time it takes for a runner to finish a marathon.

Question 15

A discrete random variable $$X$$ has the following probability distribution: $$x: 1, 2, 3$$; $$P(x): 0.6, 0.3, 0.1. $$What is the variance of $$X$$?

Accepted Answer

$$0.41$$

Question 16

When graphing a discrete probability distribution, how can you emphasize that the data is discrete?

Accepted Answer

Leave gaps between the bars in the graph.

Question 17

If $$P(X=0)=0.1$$, $$P(X=1)=0.4$$, $$P(X=2)=0.3$$, and $$P(X=3)=0.2$$, what is $$P(X\u003e1)$$?

Accepted Answer

$$0.5$$

Question 18

Which of the following best describes the horizontal and vertical axes in a graph of a discrete probability distribution?

Accepted Answer

The horizontal axis represents the values of the random variable, and the vertical axis represents the probabilities.

Question 19

A discrete random variable $$X$$ has mean $$\mu=2$$ and standard deviation $$\sigma=0.5. $$Which of the following statements is true?

Accepted Answer

Most values of $$X$$ are likely to be close to 2.

Question 20

Suppose a discrete random variable $$X$$ has possible values $$0, 1, 2$$ with probabilities $$0.5, 0.3, 0.2$$ respectively. What is the standard deviation of $$X$$?

Accepted Answer

$$0.7$$

Section 6.1 Discrete Random Variables

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