Question: Let Ni be independent Poi(i) processes, i = 1, 2 and let S1 n be the time of the nth event of the first process,

Let Ni be independent Poi(λi) processes, i = 1, 2 and let S1 n be the time of the nth event of the first process, and S2 m be the time of the mth event of the second process.

(a) What is Pr S1 1 < S2 1

(b) Using the memoryless property of the exponential, what is Pr S1 n < S2 1

, i.e. n events from process 1 occur before any from process 2?

(c) At any given time, what is the probability that the next event which occurs will come from process i, i = 1, 2?

(d) In general, what is Pr S1 n < S2 m

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