please solve these problems:

Questions 5. A box contains four bowling balls numbered 2, 4, 6, and 10 according to their weight. Two are drawn randomly without replacement. Let the random variable M denote the max of the two numbers on the balls drawn. Calculate lE(M) and Var(M). Hint: Start by specifying the joint distribution of the number on the balls. 6. Let W be a random variable that is equally likely to be any integer from 1 to 10. (a) Calculate the IE(W). (b) Calculate the Var(W). (c) Calculate the Var(10W). ) (d Calculate the variance of a random variable that is equally likely to be any integer from 1 to 100. 7. Suppose that X has a Geometric Distribution where P(x):p:rl(1p) f0r$:172737475l"' (a) (Bonus) Show that the expected value 21:2E X 1 X 2 = ( )( ) (1_p)2 by using the facts: d d2 P3:=0a.nd Pa:=0. Hints: (i) 1E(X - 1) = 23:10? - 1)P($) = Zillt - MpgW1 '10) (ii) Using (i) and the rst fact Show ]E(X 1) = (iii) Using (ii) and the second fact show ]E(X 1)(X 2) = %g (b) Use the answer from part (a) to calculate the variance of X. (c) Calculate E(aX) for some number a that is Ial