Let {X1, X2,...} be a sequence of independent and identically distributed random variables with PDF fX(x), and let N be an integer-valued random variable with PMF pN(n), where N and the Xi are independent. Consider a process in which events occur at times X1, X1 + X2,... , X1 + X2

+···+ XN .

a. Calculate the mean, variance, and s-transform of the PDF of the time of the last event.

b. What is the expected number of events in the interval (0, t)?