5. A bowl contains 10 red balls, 6 white balls, and 4 blue balls. The red balls are all marked "10", the white balls are all marked "5", and all the blue balls are all marked "0". Two (2) balls are going to be randomly selected with replacement. That is to say, you will select a ball, record the color and number marking, then put that ball back into the bowl and then select a second ball. Thus the picks are independent as well. Let X be the number of red balls picked (marked "10") and let Y be the number of White balls picked (marked "5"). a. Tabulate the joint probability mass function table (pmf values of P(X = 3:, Y = y)) for X and Y. b. The number markings indicate the amount of points you will receive when picking that ball. For example a red ball gives you 10 points. So if your two picks are a red ball and a white ball, the total you have is 15. If you pick two blue balls, your total is 0. We are interested in T, the sum of the numbers that are marked on the two balls picked. Show E(T)=13 and var(T)=30.5. c. Now suppose instead of picking just two balls, we pick n=200 balls with replacement from the bowl ( can think of this as picking 2 balls 100 times ). Let Xi denote the amount of points of the ith picked ball, for i=1,2,...,n=200. Use the Central Limit Theorem (CLT) to approximate the probability that the sum of the points \f