Given the joint probability distribution (, , ) = 9 = 1, 2, 3; = 1, 2, 3; = 1, 2 Find: i. Show that k = 1 12 ii. The joint marginal distribution of X and Y. iii. The joint conditional distribution of Y given X=3. b) If X is the amount of money (in dollars) that a personal assistant spends on coffee during a day and Y is the corresponding amount of money (in dollars) for which she is reimbursed, the joint density of these two random variables is given by (, ) = { 1 25 ( 20 1) 10 < < 20; 2 < < 0 i. the marginal density of X; ii. the conditional density of Y given X = 12; iii. Find the probability that the salesperson will be reimbursed at least $8 given that he spends $12.