Question

Assume that arrivals come from two independent Poisson processes of males and females with respective rates of λ=4/hr and µ=6/hr.

If the system is currently empty, find the probability that

(a) there will be no arrivals in the next 10 minutes;

(b) there will be no arrivals in the next 10 minutes, given the last arrival was over 9 minutes ago;

(c) there will be no males arriving in the next 10 minutes, but at least one female;

(d) a male will arrive before a female;

(e) there will be exactly 10 arrivals in the next hour;

(f) there will be exactly 10 arrivals in the next hour and at least 9 of them are female;

(g) there will be exactly 10 arrivals in the next hour, of which exactly 5 came in the last half hour

Answer 1