A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. Twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the remaining 30% choose a 65-oz box. Let X1 and X2 denote the package sizes selected by two independently selected purchasers.

a. Determine the sampling distribution of X, calculate E(X), and compare to .

b. Determine the sampling distribution of the sample variance S2

, calculate E(S2

), and compare to 2

.