## X and Y are uncorrelated.
X = rexp(1e4)
Y = rexp(1e4)
S = X + Y   ## compare mean(X)+mean(Y) to mean(S)
Z = X*Y     ## compare mean(X)*mean(Y) to mean(Z)

## U and V are correlated because they both include A.
A = rexp(1e4)
U = A + rexp(1e4)
V = A + rexp(1e4)
T = U + V   ## compare mean(U)+mean(V) to mean(T)
W = U*V     ## compare mean(U)*mean(V) to mean(W)