Consider the following distribution of the two random variables (X, Y) Y\X 0 1 2 0 0.10 0.35 0.20 1 0.05 0.10 0.20 Furthermore, let (X, Y), i = 1, 2,... be independent pairs of random variables, with each pair (X, Y) distributed like (X, Y). (a) (8 pts) Determine the probability distribution of the random variable X - 2Y. (b) (5 pts) What does the law of large numbers imply about the distribution of 800 1 800 2017 i1 (c) (5 pts) What is the probability that Y > X? (d) (5 pts) What is the probability that Y > X? (e) (8 pts) What is the probability distribution of X conditional on the event that at the same time, Y =0 and X>0? (f) (9 pts) Is the conditional mean E[YIX ] a linear function of r? Explain. =