Exdx xexdx let denote the time until the next train arrives and uniform

E [W] = Z 1 E [W|X = x] λe−λxdx

= Z T E [W|X = x] λe−λxdx + Z 1 E [W|X = x] λe−λxdx

(a) E [X] = E [E [X|T]] = E [7T] = 7/2.

(b) Note that E [X|T] = 7T and Var (X|T) = 7T. By the conditional variance formula

type of year, be as given in (a).

(d) No! Knowing how many storms occur in an interval changes the probability that it is a