1. Suppose Xi are independent random variables and that E(Xi) =mu , Var(Xi) = sigma^2. (a) What is the mean of (X-bar)^2?

1. Suppose Xi are independent random variables and that E(Xi) =mu , Var(Xi) = sigma^2.

(a) What is the mean of (X-bar)^2?

(b) Prove that (X-bar)^2 converges in probability to a constant and give that constant.

State any theorems or results you use in your proof.

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