What is the distribution of the time till the next epoch of, Advanced Statistics

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What is the distribution of the time till the next epoch of

Message : 1) Let N1(t) and N2(t) be independent Poisson processes with rates, ?1 and ?2, respectively. Let
N (t) = N1(t) + N2(t).

a) What is the distribution of the time till the next epoch of N2(t)?

b) What is the probability that the next epoch of N (t) is an epoch in N1(t)?

c) What is the distribution of the next epoch of N (t)?

d) What is the mean number of N1(t) epochs before the next epoch of N2(t)?

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