Urns: Suppose um H is lled with 40% green balls and 60% red balls, and urn T is lled with 60% green balls and 40% red balls. Someone will ip a coin and then select a ball from urn H or urn T depending on whether the coin lands heads or tails, respectively. Let X be 1 or i] if the coin lands heads or tails, and let Y be 1 or i] if the ball is green or red. at} Write out the joint distribution of X and Y in a table. b} Find E[Y]. What is the probability that the ball is green? c} Find VaI[Y|X = D], Var[Y|_X = 1] and Var[Y]. Thinking ofvarianceas measuring uncertainty, explain intuitively why one of these variances: is larger than the others. d} Suppose you see that the ball is green. What is the probability that the coin turned up tails