Question: Would appreciate an answer to this question! 1. This question has two unrelated parts: (a) Let (Xt ) and (Yt ) be independent Poisson processes

Would appreciate an answer to this question!

1. This question has two unrelated parts: (a) Let (Xt ) and (Yt ) be independent Poisson processes with rates a and u. Using thinning/superposition, find the probability that the process (Xt, Y) ever visits the state (i, j). [2] (b) Let (Nt, t > 0) be a renewal process. Let m(t) = E(Nt ) denote the expected number of events observed by time t. Let F (x) = P(t

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