Question: Problem 11. Let X 1 , X 2 be i.i.d. normal random variables with mean zero and variance 1 Let U= X 1 -X 2

Problem 11.

Let X1 , X2 be i.i.d. normal random variables with mean zero and variance 1

Let U= X1-X2, V=X2-X1. Show that U and V are independent

Problem 12.

Let Xi,i=1,...,n be i.i.d. mean zero and variance 1 random variables

Show that the sample mean and sample variance of all the X's are independent.

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