2. Suppose Yı, ... Yn are iid normal random variables with normal distribution with unknown mean and variance, and 02. L

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2 Suppose Yi Yn Are Iid Normal Random Variables With Normal Distribution With Unknown Mean And Variance And 02 L 1 (149.55 KiB) Viewed 109 times

2. Suppose Yı, ... Yn are iid normal random variables with normal distribution with unknown mean and variance, and 02. Let y = 121=1Y;. For this problem you may not assume that n is large. (a) What is the distribution of ? (b) What is the distribution of 2 = (*=+)* + (*=4) + (*=4) ?? Let s2 = n-1 2-1(Y; - Y)? (e) What is the distribution of (n-1)o? () What is the distribution of vacy –+)? Show how you derived this from the definition of the distribution you used. (e) Let Z1 = (*1=4) * + (x+4)*+ (**) *, 22 = (x+4)* + (*-4). What is the distribution of W = 2: ? Show how you derived this from the definition of the distribution you used. (f) What is the expected value of 2 = Y1 + 2Y2 + ... + nYn? (g) What is the variance of 2 = Y + 2Y2 +...+ nYn? (h) What is the covariance of Z1 = Y1 + 2Y2 and Z2 = 2Y1 +Y2?