Question: 1.4. Consider a renewal process for which the lifetimes X,, X,, ... are discrete random variables having the Poisson distribution with mean A. That is,

1.4. Consider a renewal process for which the lifetimes X,, X,, ... are discrete random variables having the Poisson distribution with mean A.

That is, e-An Pr{Xk=n}_ A forn=0,1,....

n!

(a) What is the distribution of the waiting time Wk?

(b) Determine Pr{N(t) = k).

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