Question

(1) Busy car wash Suppose you run a (busy) car wash, and the number of cars that come to the car wash between time 0 and time s > 0 is a Poisson process with rate λ = 1. The number of red cars that come to the car wash between time 0 and time s > 0 is a Poisson process with rate 2. The number of blue cars that come to car wash between time 0 and time s > 0 is a Poisson process with rate 3. Both Poisson processes are independent of each other. All cars are either red or blue.

(i) With what probability will five blue cars arrive, before three red cars have arrived?

(ii) Suppose each car is equally likely to have one, two, three, or four people in it. What is the average number of cars with four people that have arrived by time s = 100?

(iii) Suppose each car is equally likely to have one, two, three, or four people in it. What is the expected number of all passengers of cars that arrived to the car wash by time s = 100?

PLEASE ANSWER (iii) PLEASE!!

Answer 1

Solution given data, -hom the Supen poshon, Cars auive with the Habe the Q+3=5 So by thinking that, the Cars with the tour people 1ale ariive at 은 (100) 25 So, 4 25