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Suppose that X1,X2 and X3 are independent random variables with common mean E(Xi) = μ and...

Suppose that X1,X2 and X3 are independent random variables with common mean E(Xi) = μ and variance Var(Xi) = σ2. Let V= X2−X3 and W = X1− 2X2 + X3.

(a) Find E(V) and E(W).

(b) Find Var(V) and Var(W).

(c) Find Cov(V,W).

(d) Find the correlation coefficient ρ(V,W). Are V and W independent?

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