For this problem you may require the Schwarz inequality. Given any two rv X and Y with finite variances, the Schwarz inequality states that [E(XY)] [E(X)E(Y)]. < For a rv Z which is positive, i.e. Z 0, show that P(Z > a) > (E(Z) - a) E(Z) where a > 0 is any arbitrary constant. (Hint: think of a rv which converts into a probability upon taking expectations.)