Starting at timet=0 , cars arrive at a car wash according to a Poisson process with rate ofcars/hour. At any given moment, the car wash is either free or occupied. The car wash is initially free at timet=0 . If a car arrives at the car wash when it is free, the car is serviced immediately. Service lasts for1/4hours, during which the car wash is occupied. If a car arrives at the car wash when it is occupied, the car is denied service and it leaves the car wash.

Whenever necessary, write down your answers using the standard notation. Type fact(n) forn! .

1. Write down the PMFpN(k)ofN , the number of cars arriving at the car wash between times0and3 , in terms ofandk .

Fork=0,1,... ,

p_N(k) = ?