Let N 1 ,...,N m be independent Poisson processes on R+ with location-dependent rates λ 1 (t),...,λ m (t), respectively. Let τi denote the time of the first occurrence in process Ni. Find the...

Let N₁,...,N_m
be independent Poisson processes on R+ with location-dependent rates λ₁(t),...,λ_m(t), respectively. Let τi denote the time of the first occurrence in process Ni. Find the distribution of τ = min1≤i≤m τi. Find P{τi = τ}