Suppose that (X1, Y1), , (Xn, Yn) form a random sample from a bivariate normal distribution with means x and y, variances 2x and 2y, and correlation Let R be the sample correlation Prove that the distribution of R depends only on , not on x, y, 2x, or 2y

Question: Suppose that (X1, Y1), . . . , (Xn, Yn) form a random sample from a bivariate normal distribution with means x and y, variances

Suppose that (X1, Y1), . . . , (Xn, Yn) form a random sample from a bivariate normal with means μx and μy, variances σ2x and σ2y, and correlation ρ. Let R be the sample correlation. Prove that the of R depends only on ρ, not on μx, μy, σ2x, or σ2y.

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