8. (15 points, 5+5+5) Suppose the heights of a high school students X ~ N(55, 64). Using probability Table V, (1). Find P(52 50). (3). Find P[(X - 53) (X -59) > 0]9. (10 points, 3+3+2+2) Let random vector (X, Y ) have the following joint probability mass function X Y =1 2 3 0.1 0.05 0 2 0.15 y 0.1 0.05 0.05 0.05 y 0.1 2 Z (1). Find the values of x, y and z. (2). Find P(X = 2Y - 3). (3). Find P(Y = 1/X > 2). (4). Are random variables X and Y independent? Why