1. At the office of a college provost, calls arrive at extension 1247 according to a Poisson process



N1(t) : t ≥ 0

with rate λ, and calls arrive at extension 1223 independently according to a Poisson process



N2(t) : t ≥ 0

with rate μ. Let N be the number of calls arriving at extension 1223 between two consecutive calls made to extension 1247.

Find the probability mass function of N.

Hint: Let X be the period between two consecutive calls made to extension 1247.We are interested in P

????

N2(X) = i

, i ≥ 0.