APFIVE Properties of Combined Independent Variables
A joint probability mass function of X and Y is given by P(X=x, Y=y) = P(X=x)P(Y=y) for all values of x and y. If Z = X + Y and W = X - Y, which statement about Z and W is necessarily true?
A
Cov(Z,W) must equal zero
B
Z and W are not necessarily independent
C
Var(Z) = Var(W)
D
Z and W must be independent
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