A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz. T...

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 ),and compare to m.

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