Let X1,X2,X3 be random variables such that E(Xi) = μ and Var(Xi) = σ2 for all i. Find the value of the following quantities (as a function of μ and σ2) if the Xis are all mutually independent. Then repeat these calculations if each pair of variables have a correlation of ρ, that is, corr(Xi, Xj ) =ρ for i ≠ j. (a) E(X1 −X2 +X3) (b) Var(X1 − X2 + X3) (c) E(X21 − X22 + X23)

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