Problem 1 Simulate two Poisson processes Ni(t) and N2(t). Nj has mean rate )1 = 1 and N2 has mean rate 12 = 2. You should: a) Show the code (or pseudo-code) b) Estimate by Monte Carlo simulation (with 1000 scenarios) E[N1(t)], E[N2(t)], Var[Ni(t)], Var[N2(t) ] for t = 10. Hint: first generate the interarrival times 71(w), 72(w), ....which are expo- nential with parameter / by inversion. For instance, if U is uniform T1 ( W ) = F, 1(U(W) ) where F is the inverse of the exponential distribution function