Poisson distribution car crash

Question

Car crashes at a traffic stop arrive follows a Poisson Process with rate lambda = 2/hr.

(a) Expected amount of time until the 2nd car crash arrives

Why is the expected amount of time until the second car crash is 1 hour? How did we get that number?

b) If car crashes arrive at another traffic stop according to Poisson Process with rate 3/hr, find expected time we wait until a car crash occurs at either traffic stop. Why is this 1/5?

Answer 1

• Remember that for a poisson process, the interarrival time follows exponential distribution with mean $\frac1\lambda$.

Let $X_1$ be the time until the first crash and let $X_2$ be the time until the second crash from the first crash.

You just have to compute $E[X_1+X_2]$.