Problem 3 (Probability Inequalities) State whether the statements can be labeled with : if equality always holds, and similarly label it with 2 or 3 if one of these hold. If no such inequality or equality holds, then label the statement as NONE. Please note that your labeling should be accompanied by a justication. a. py (903)) versus pX (x) if Y : g(X), where X is a discrete random variable. b. Let X be exponentially distributed with parameter A. Show by elementary integration that [[4100] = A/(A jt). c. {[[X][E[Y]}2 versus [E[X2Y2] if X and Y are uncorrelated jointly Gaussian random variables. (1. [E[log2(1 + \\/X)] versus 1 if X 2 0 and [E(X) g 1. e. If [[X] = 17 compare [EH2X 1|] and 1. f. X is a continuous random variables with fX($) : fX(:z:) and [E[|X|] : 1. Compare [P[X 2 4] and 1/8