Question: Foruncorrelatedrandomvariables U, V , and W, let X = U + V and Y = U +W. (a) Showthatcov(X,Y ) = var(U) and (b) Forsomescaling,suppose

Foruncorrelatedrandomvariables U, V , and W, let X = U + V and Y = U +W.

(a) Showthatcov(X,Y ) = var(U) and

(b) Forsomescaling,suppose X = math achievementtestscore, Y = verbalachievementtest score, U = intelligence(e.g.,IQ), V = time studyingmath, W = time studyingverbal.
Explain howcorr(X,Y ) changesasvar(U) increases, forfixedvar(V ) and var(W).

corr(X,Y) = var(U) [var(U)+var(V)][var(U) + var( + var(W)]

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