Consider the population described by the probability distribution shown below. x 1 2 3 4 5 p1x2 .2 .3 .2 .2 .1 The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as shown below Sample Probability Sample Probability 1, 1 .04 3, 4 .04 1, 2 .06 3, 5 .02 1, 3 .04 4, 1 .04 1, 4 .04 4, 2 .06 1, 5 .02 4, 3 .04 2, 1 .06 4, 4 .04 2, 2 .09 4, 5 .02 2, 3 .06 5, 1 .02 2, 4 .06 5, 2 .03 2, 5 .03 5, 3 .02 3, 1 .04 5, 4 .02 3, 2 .06 5, 5 .01 3, 3 .04

a. Find the sampling distribution of the sample mean x.

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

c. What is the probability that x is