69. Let {N(t), t 0} be a Poisson process with rate . For s < t,

69. Let {N(t), t  0} be a Poisson process with rate λ. For s < t, find

(a) P(N(t) > N(s));

(b) P(N(s) = 0,N(t) = 3);

(c) E[N(t)|N(s) = 4];

(d) E[N(s)|N(t) = 4].