Find the gap in the Cauchy-Schwarz inequality [E[XY]|

Find the gap in the Cauchy-Schwarz inequality S (the difference between IE[XYII and for the cases: (a) Y = ax for some constant a in R, X has an exponential distribution with parameter A. (b) (X, Y) are uniformly distributed over a triangle with vertices (0,0), (1,0), (0,1). (c) (X, Y) is a discrete random vector that takes values equally likely over the three points (0,0), (1,0), (0,1)