Chapter 5: Probability and Random Variables

Simulation. Refer to the probability distribution displayed in Table 5.11 on page 222 .

a. Use the technology of your choice to repeat the simulation done in Example 5.18 on page 223 .

b. Obtain the proportions for the number of heads in three tosses and compare them to the probability distribution in Table 5.11.

c. Obtain a histogram of the proportions and compare it to the probability histogram in Fig. 5.22 (b) on page 223 .

d. What do parts (b) and (c) illustrate?

Refer to the probability distribution displayed in Table \(5.11\) on page \(222\).

a. Use the technology of your choice to repeat the simulation done in Example \(5.18\) on page \(223\).

b. Obtain the proportions for the number of heads in three tosses and compare them to the probability distribution in Table \(5.11\).

c. Obtain a histogram of the proportions and compare it to the probability histogram in Fig. \(5.22\)(b) on page \(223\).

d. What do part (b) and (c) illustrate?

What concept does the mean of a discrete random variable generalize?

Comparing Investments. Suppose that the random variable X and Y represent the amount of return on two different investments. Further suppose that the mean of X equals the mean of Y but that the standard deviation of X is greater than the standard deviation of Y.

Part (a) On average, is there a difference between the return of the two investments? Explain your answer

Part (b) which investment is more conservative? Why?

In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.

Part (a) Find the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.

In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.

Part (a) Find the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.

In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.

Part (a) Find the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.

In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.

Part (a) Find the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.

Persons Per Housing Unit. The random variable Y is the number of person living in a randomly selected occupied housing unit. Its probability distribution is as follows.

Part (a) Find and interpret the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10

Part (c) Construct a probability histogram for the random variable, locate the mean: and show one, two, and three standard deviation intervals.

Space shuttles. The random variable X is the crew size of a randomly selected shuttle mission between April 12, 1981 and July 8, 2001. Its probability distribution is as follows.

Part (a) Find and interpret the mean of the random variable.

Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10

Part (c) Construct a probability histogram for the random variable, locate the mean: and show one, two, and three standard deviation intervals.