Refer to the matched-pairs experiment of Section 12.3 and assume that the measurement

Chapter 12, Problem 12.31

(choose chapter or problem)

Refer to the matched-pairs experiment of Section 12.3 and assume that the measurement receiving treatment i, where i = 1, 2, in the jth pair, where j = 1, 2,..., n, is Yi j = i + Pj + i j, where i = expected response for treatment i, for i = 1, 2, Pj = additive random effect (positive or negative) contribution by the jth pair of experimental units, for j = 1, 2,..., n, i j = random error associated with the experimental unit in the jth pair that receives treatment i. Assume that the i js are independent normal random variables with E(i j) = 0, V(i j) = 2; and assume that the Pjs are independent normal random variables with E(Pj) = 0, V(Pj) = 2 p . Also, assume that the Pjs and i js are independent. a Find E(Yi j). b Find E(Yi) and V(Yi), where Yi is the mean of the n observations receiving treatment i, where i = 1, 2. c Let D = Y 1 Y 2. Find E(D), V(D), and the probability distribution for D