Question: Let X u...,Xn be independently and identically distributed normal random variables with mean |x and variance a 2. (a) Show that is an n x

Let X u...,Xn be independently and identically distributed normal random variables with mean |x and variance a 2.

(a) Show that

S = X'AX where x = (X....X)'. A 1 n n n

is an n x n idempotent matrix of rank n - 1 .

(b) Using Exercise 12, show that S2 /cr2 is distributed as chi-square with n — 1 degrees of freedom.

S = X'AX where x = (X....X)'. A 1 n n n n n n 1 == n

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