1 Let (X1,Y1), (X2,Y2), , (Xn,Yn) be a random sample from a bivariate normal population with EX 1, EY 2, var(X) var(Y) 2, and cov(X,Y) 2 Let X,Y denote the corresponding sample means, S2 1,S2 2, the corresponding sample variances, and S11, the sample covariance Write R 2S11 (S2 1 S2 2) Show that th...

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1. Let (X1,Y1), (X2,Y2), . . . , (Xn,Yn) be a random sample from a bivariate normal...

Question:

1. Let (X1,Y1), (X2,Y2), . . . , (Xn,Yn) be a random sample from a bivariate normal population with EX = μ1, EY = μ2, var(X) = var(Y) = σ2, and cov(X,Y) = ρσ2. Let X,Y denote the corresponding sample means, S2 1,S2 2, the corresponding sample variances, and S11, the sample covariance. Write R=2S11/(S2 1+S2 2). Show that the PDF of R is given by f (r) =

√

πΓ

n−1

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