수 04 5월 2016

Q. Suppose that each event of a Poisson process \(X(t)\) with rate \(\lambda\) is classified as being either of type \(1, 2, ..., k\). If the event occurs at time \(s\), then independently of all else, it is classified as type \(i\) with probability \(p_i(s)\). Note that the probability \(p_i(s)\) depends on the event arrival time \(s\). Let \(N_i(t)\) denote the number of type \(i\) arrivals in \([0, t]\). What is the probability distribution of \(N_i(t)\), \(Pr{N_i(t)=n}\)?

A.

Category: quiz Tagged: system analysis quiz markov chain transition probability diagram