Question

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 indpendently selected purchasers.

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

Answer 1

The sample variance is shown in the attached documents. Also E(S2) = 212.5 and σ2 is also 212.5 (they're the same when compared)

They are the same when compared.

Explanation:

STEP 1.

The probability of selecting each of the three sizes of soap 25 oz, 40 oz, and 65 oz are 20% = 0.20, 50% = 0.50 and 30% = 0.30 respectively

PLEASE FIND THE ATTACHED DOCUMENTS FOR DETAILED SOLUTION AND EXPLANATION TO Determine the sampling distribution of the sample variance S2, calculate E(S2), and compare to σ2

From the attached documents, E(S2) = 212.5 and σ2 is also 212.5

They are the same when compared.