Cars arrive at a tollbooth at a rate of 5 cars every 10 minu

Cars arrive at a tollbooth at a rate of 5 cars every 10 minutes, beginning at midnight.

(a) What is the distribution of the random variable T, the time when the first car arrives? Evaluate E(T) and Var(T).

(b) Use the distibution of T to compute the probability that the first car arrives by 12:01a.m.

(c) Use a Poisson random variable to answer (b)

Solution