Prove that

(a) max(X1, X2) = X1 + X2 − min(X1, X2) and, in general,

(b) max(X1,..., Xn) = n 1

Xi −

i< j min(Xi, X j)

+



i< j

+(−1)

n−1 min(Xi, X j,..., Xn)

(c) Show by defining appropriate random variables Xi , i = 1,..., n, and by taking expectations in part

(b) how to obtain the well-known formula?