Question: Prove that if x1, x2, ..., x, is a random sample of size n from N(, ), then x-x is independent of x and hence

Prove that if x1, x2, ..., x, is a random sample of size n from N(, ), then x-x is independent of x and hence (x,-x) of x. Use this result to prove an extension of the result of $5.3 that (x;-)/02 is x with n degrees of freedom; namely that (x-x)/0 is x with (n-1) degrees of freedom.

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