52. Let Xi , i = 1, 2, . . . , be the interarrival times of the renewal process {N(t)}, and let Y, independent of the Xi , be exponential with rate λ.

(a) Use the lack of memory property of the exponential to argue that P{X1 + · · · + Xn n

(b) Use part

(a) to show that

where X has the interarrival distribution.

Transcribed Image Text:

E[N(Y)] = E[e-XX] 1- Ele-xx]