Question: 1.*10. Let {Xj , j > I} be a sequence of independent r.v.'s having the common exponential distribution with mean 1 lA, A > 0

1.*10. Let {Xj , j > I} be a sequence of independent r.v.'s having the common exponential distribution with mean 1 lA, A > 0 For given x > 0 let v be the maximum of n such that Sn < x, where So = 0, Sn = 2:J=l Xj as usual. Prove that the r.V. v has the Poisson distribution with mean AX. See Sec. 5.5 for an interpretation by renewal theory.

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