A large but sparsely populated county has two small hospitals, one at the south end of the county and one at the north end. The south hospital emergency room has four beds, whereas the north hospital emergency room has only 3 beds. Let X denote the number of south beds occupied at a particular time on a given day. Let Y denote the number of North beds occupied at the same time on the same day. Suppose that these two random variables are independent; that the pmf of it puts probability masses .1, .2, .3, .2 and .2 on x values of 1,2,3,and 4 respectively; and that the pmf of 'I" distributes probabilities .1, .3, .4 and .2 on the y values D, 1, 2, and 3, respectively. a. Display the joint pmf of X and Y in a joint probability table. b. Compute P[x