Consider the population described by the probability distribution shown below. The random variable x is observed twice with independent observations.

x 0 1 2 3 p1x2 0.3 0.2 0.3 0.2 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 follows:

Sample Probability Sample Probability 0, 0 0.09 2, 0 0.09 0, 1 0.06 2, 1 0.06 0, 2 0.09 2, 2 0.09 0, 3 0.06 2, 3 0.06 1, 0 0.06 3, 0 0.06 1, 1 0.04 3, 1 0.04 1, 2 0.06 3, 2 0.06 1, 3 0.04 3, 3 0.04

a. Complete the sampling distribution table. Type the values of x in ascending order.

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

c. What is the probability that x is 3 or larger?

d. Would you expect to observe a value of x equal to 3 or larger?