4 Let (X1,Y1), , (Xn,Yn) be a sample from a bivariate normal distribution with parameters EX1 1, EYi 2, var(Xi) var(Yi) 2, and cov(Xi,Yi) 2, i 1,2, ,n Find the distribution of the statistic T(X,Y) n (X1)(Y 2) 4n i 1(XiYiX Y)

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Question: 4. Let (X1,Y1), . . . , (Xn,Yn) be a sample from a bivariate normal distribution with parameters EX1 = 1, EYi = 2, var(Xi)

4. Let (X1,Y1), . . . , (Xn,Yn) be a sample from a bivariate normal distribution with parameters EX1 = μ1, EYi = μ2, var(Xi) = var(Yi) = σ2, and cov(Xi,Yi) = ρσ2, i = 1,2, . . . ,n. Find the distribution of the statistic T(X,Y) =

√

(X−μ1)−(Y −μ2) 4n i=1(Xi−Yi−X+Y)

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