Suppose that (Xi , Yi), i 1, , n, form a random sample of size n from the bivariate normal distribution with means 1 and 2, variances 21 and 22 , and correlation Determine the mean and the variance of the following statistic T , given the observed values X1 x1, , Xn xn T

Question: Suppose that (Xi , Yi), i = 1, . . . , n, form a random sample of size n from the bivariate normal distribution

Suppose that (Xi , Yi), i = 1, . . . , n, form a random sample of size n from the bivariate normal with means Î¼1 and Î¼2, variances Ïƒ21 and Ïƒ22 , and correlation Ï. Determine the mean and the variance of the following statistic T , given the observed values X1 = x1, . . . , Xn = xn:

- T =- -

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