수 04 5월 2016

Q. Consider an elevator that starts in the basement (floor \(0\)) and travels upward. Let \(N_i\) denote a random variable representing the number of people that get in the elevator at floor \(i\). Assume that \(N_i\)'s are independent and that \(N_i\) is Poisson with mean \(\lambda_i\). Each person entering at \(i\) will, independent of everything else, get off at \(j\) with probability \(P_{ij}(\sum_{j>i}P_{ij}=1)\). Let \(O_j\) be the number of people getting off the elevator at fllor \(j\).

(a) Compute \(E[O_j]\)

(b) What is the probability distribution of \(O_j\)?

A.

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