The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency: x 0 2 4 6 p1x2 1 4 1 4 1 4 1 4

a. List all the different samples of n = 2 measurements that can be selected from this population. For example, (0, 6) is one possible pair of measurements; (2, 2) is another possible pair.

b. Calculate the mean of each different sample listed in part

a. c. If a sample of n = 2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected?

d. Assume that a random sample of n = 2 measurements is selected from the population. List the different values of x found in part b and find the probability of each. Then give the sampling distribution of the sample mean x in tabular form.

e. Construct a probability histogram for the sampling distribution of x.