3. (S & W Chapter 2: 2.9) X and Y are discrete random variables with the following joint distribution: Value of Y 14 22 30 40 65 0.02 0.05 0.10 0.03 0.01 Value of X 5 0.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 0.09 That is, Pr (X=1, Y=14) = 0.02, and so forth. a) (5 points) Calculate the probability distribution, mean, and variance of Y. b) (5 points) Calculate the probability distribution, mean, and variance of Y given X=8. c) (5 points) Calculate the covariance and correlation between X and Y. 4. In a population, My=100 and of=22. Using the central limit theorem, answer the following questions (write your final answer in terms of ): a) (5 points) In a random sample of n=100, find Pr(Y 99)