Suppose x equals the number of heads observed when a single coin is tossed; that is, x = 0 or x = 1. The population corresponding to x is the set of 0s and 1s generated when the coin is tossed repeatedly a large number of times. Suppose we select n = 2 observations from this population. (That is, we toss the coin twice and observe two values of x.)

a. List the three different samples (combinations of 0s and 1s) that could be obtained.

b. Calculate the value of x for each of the samples.

c. Show that the sample proportion of 1s, pn, is equal to x.

d. List the values that pn can assume, and find the probabilities of observing these values.

e. Construct a graph of the sampling distribution of pn.