a) Prove that for any constant Q, (X-X)Q=0 i=1 b) Use (a) to prove, N N...

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a) Prove that for any constant Q, Σ(X₁-X)Q=0 i=1 b) Use (a) to prove, N N Σ(X₁-X)(Yi-Y) = Σ(X₁-X)Yi i=1 i=1 c) Prove that E(X) = μx. d) Prove that Var (X) = 0²/N for iid X₁. What happens as N→ ∞o? e) Suppose that X₁, X2,..., Xy is an iid sample of data. Prove the following is an unbiased estimator for the variance, ²: N 1 N-1 Σ(x − x)2 a) Prove that for any constant Q, Σ(X₁-X)Q=0 i=1 b) Use (a) to prove, N N Σ(X₁-X)(Yi-Y) = Σ(X₁-X)Yi i=1 i=1 c) Prove that E(X) = μx. d) Prove that Var (X) = 0²/N for iid X₁. What happens as N→ ∞o? e) Suppose that X₁, X2,..., Xy is an iid sample of data. Prove the following is an unbiased estimator for the variance, ²: N 1 N-1 Σ(x − x)2

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ANSWER UUGEO b C WINE J X X Q i1 X Q 2 i1 n X XQ 1 i1 ... View the full answer