Bivariate pdf (a) Find the marginal probability mass functions of X and Y. Using these distributions, compute E[X], Var(X), E[Y] and l'ar(Y). (b) Compute the conditional pmf f (3:|Y : 0) and f (y|X = 2), and also write down the marginal pmf f (cc) and f (y) for comparison. (c) Are X and Y independent? Fully justify your answer. ((1) Compute E [X Y=O]. E[Y X = 2], l"a-r[X Y = 0], l'ar[Y X = 2] and Co-v(X, Y). (e) Now suppose X and Y represent outcomes of two lotteries, and you would like to invest your $1 to these lotteries. Assume you are extremely risk averse, hence only care about the risk (preferably 10W variance) of your investment. How do you want to distribute your $1, i.e., how do you choose your a E [0.1] for (1X + (1 MY