How do you go about proving this:
Consider random variables X, Y, Z with Z ? Bernoulli(1/2), X ? Unif(0, 1), and Y ? Unif(0, 1).
Prove or disprove the following statement: Cov(X, Y ) > 0 E(Cov(X, Y |Z)) > 0.
Consider random variables X, Y, Z with Z ? Bernoulli(1/2), X ? Unif(0, 1), and Y ? Unif(0, 1).
Prove or disprove the following statement: Cov(X, Y ) > 0 E(Cov(X, Y |Z)) > 0.
