If Xi,i = 1, 2, 3, are independent exponential random variables with rates i , i =

If Xi,i = 1, 2, 3, are independent exponential random variables with rates λi , i = 1, 2, 3, find

(a) P{X1 < X2 < X3},

(b) P{X1 < X2| max(X1, X2, X3) = X3},

(c) E[max Xi|X1 < X2 < X3],

(d) E[max Xi].