1. Let



N1(t) : t ≥ 0

and



N2(t) : t ≥ 0

be independent Poisson processes with rates

λ and μ, respectively. For n,m ≥ 1, find the probability that the  nth event of the process N1(t) : t ≥ 0

occurs before the mth event of the process



N2 : t ≥ 0

.