Toss three fair coins and let x equal the number of heads observed.

a. Identify the sample points associated with this experiment and assign a value of x to each sample point.

b. Calculate p1x2 for each value of x.

c. Construct a graph for p1x2.

d. What is P1x = 2 or x = 32? NW M04_MCCL3396_14_GE_C04.indd 218 29/09/2021 14:00 SECTION 4.2 ● Probability Distributions for Discrete Random Variables 219 Applet Exercise 4.1 Use the applet Random Numbers to generate a list of 25 numbers between 1 and 3, inclusive. Let x represent a number chosen from this list.

a. What are the possible values of x?

b. Write a probability distribution for x in table form.

c. Use the probability distribution in part b to find the expected value of x.

d. Let y be a number randomly chosen from the set 51, 2, 36. Write a probability distribution for y in table form and use it to find the expected value of y.

e. Compare the expected values of x and y in parts c and

d. Why should these two numbers be approximately the same? Applet Exercise 4.2 Run the applet Simulating the Probability of a Head with a Fair Coin 10 times with n = 2, resetting between runs, to simulate flipping two coins 10 times. Count and record the number of heads each time. Let x represent the number of heads on a single flip of the two coins.

a. What are the possible values of x?

b. Use the results of the simulation to write a probability distribution for x in table form and then use it to find the expected value of x.

c. Explain why the expected value in part b should be close to 1.