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  3. 2 suppose i 2 let y are iid normal random...

Question: 2 suppose i 2 let y are iid normal random...

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2. Suppose i, ơ2. Let Y are iid normal random variables with nornnal distribution with unknown mean and variance, μ and is: 1 . For this problem you may not assume that n is large. n (a) What is the distribution of Y? (b) What is the distribution of z-(ga), (n-e), (y, e)2? (c) What is the distribution of (a- (d) What is the distribution ofw)? Justify your answer. (e) Let Zi (y e) 2 (3 ) 2 + (y )2 Z2 = (Y μ) 2 + (n-2). What is the distribution of Ws Justify your answer. (f) what is the expected value of Z = Yi + 2 + . . . + nYG2 (g) what is the variance of Z = Y1 + 2½ + . . . + n ?

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