Question: Problem 5.53 Let X(t) be a Poissont process with intensity . (a) Show that limt E X(t) t 2 = 0. (b) Use

Problem 5.53 Let X(t) be a Poissont process with intensity λ.

(a) Show that limt→∞ E X(t) t − λ 2 = 0.

(b) Use Chebyshev’s inequality and part

(a) to show that for every d > 0 limt→∞ P  X(t) t − λ > d = 0.

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