Two types of items arrive at a station for processing according to independent Poisson processes with respective rates λ and λ . Let Tm and T  n denote the times of the mth and nth arrivals from the...

Two types of items arrive at a station for processing according to independent Poisson processes with respective rates λ and λ . Let Tm and T  n denote the times of the mth and nth arrivals from the two respective processes. Show that P{Tm
²
n} = P{Y ≥ m}, where Y has a binomial distribution with parameters m + n − 1 and λ/(λ + λ` ).