Let X1, . . . , Xn be random variables corresponding to n independent bids for an item on sale. Suppose each Xi is uniformly distributed on [100, 200]. If the seller sells to the highest bidder, what is the expected sale price?
A)Find the pdf of W = Max (X1, X2, …, Xn).
B) Find E(W).
Hint: Let W = Max (X1, X2, …, Xn).
1. P[W ≤ c] = P[Max (X1, X2, …, Xn) ≤ c] = P[X1 ≤ c, X2 ≤ c,…, Xn ≤ c]
2. Obtain the pdf of W by differentiating its cdf of W.