1. Suppose that P(x, v) , the joint probability mass function of X and Y , is given by P(2,1) = 0.2, P(2,2) = 0.1, P(3,1) = 0.3, P(3,2) = 0.25, P(3,3) = 0.15. (a) (5 Marks) Find the cumulative distribution function of Y. (b) (5 Marks) Find the third moment of Y. (c) (5 Marks) Find the conditional means of X given different values of Y. (d) (5 marks) Calculate the correlation coefficient of X and Y