Let X1, . . . , X10 be random variables denoting 10 independent bids for an item that is for sale. Suppose each Xi is uniformly distributed over the interval [100, 200]. If the seller sells to the highest bidder, how much can he expect to earn on the sale? (Hint: Let Y = max(X1, . . . , X10). First, find the cdf FY (y) of Y by noting that, in view of independence, P(Y ≤ x) = P(X1 ≤ x, . . . , X10 ≤ x) = P(X1 ≤ x). . . P(X10 ≤ x). Then obtain the pdf fY (y) of Y , and use the classical formula defining E(Y ).)
