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 µ.
b. Determine the sampling distribution of the sample variance S2, calculate E(S2), and compare to σ2.