1) Suppose two fair dice are tossed. Find the expected value of the product of the faces showing.
2) Suppose that fx,y(x,y) = 2/3(x+2y), x and y are in [0,1]. Find Var(X+Y)
3) A gambler plays n hands of poker. If he wins the kth hand, he collects k dollars; if he loses the kth hand, he collects nothing. Let T denote his total winnings in n hands. Assuming that his chances of winning each hand are constant and are independent of his success or failure at any other hand, find E(T) and Var(T).