42. Let {N(t), t 0} be a Poisson process with rate . Let Sn denote the time...

42. Let {N(t), t 0} be a Poisson process with rate λ. Let Sn denote the time of the nth event. Find

(a) E[S4],

(b) E[S4|N(1) = 2],

(c) E[N(4) − N(2)|N(1) = 3].