Question: 10. Prove that if X = X1 + + Xn and Y = Y1 + + Yn, where Xi

10. Prove that if X = X1 + · · · + Xn and Y = Y1 + · · · + Yn, where Xi and Y j are independent whenever i 6= j , then cov(X, Y ) =

Pn i=1 cov(Xi , Yi ). (Assume that all series involved are absolutely convergent.)

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