Question: For k 1, let Tk be the arrival time for the k-th arrival for a Poisson process with rate . (a) Find the joint density

For k 1, let Tk be the arrival time for the k-th arrival for a Poisson process with rate .

(a) Find the joint density of (Tm, Tn) for m < n.

(b) Find the conditional density of Tm given Tn = t.

(c) Let Wk = Tk Tk1 for k 1 (where T0 = 0). Compute P(W1 < W2 < . . . < Wn1 | Tn = t)

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