4. (10 points) For two random variables X and Y, if E(X) = 1, E(X2) = 5, E(Y) = 3, E(Y2) = 11, E(XY) = 4. What is the value of the variance Var(5Y 2X)? 2. (20 points) In a piston assembly, the specications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability distribution is given in the table below: y 1 2 3 .12 .11 .10 .07 .05 .04 .05 .04 .02 .03 .02 .01 (a) What is P(X = Y), that is, the numbers with too little clearance and too much clearance are the same? (b) What is the probability that the total number of too little clearance and too much clearance is no more than 3'? (c) Find Var(X) and Cov(X, Y)