Traffic with Poisson distribution The number of cars that cross an intersection during any interval of length t minutes between 3:00 pm and 4:00 pm has a Poisson distribution with mean t. Let W be the time that has passed after 3:00 pm and before the first car crosses the intersection. What is the probability of W being less than two minutes?

Hint: The probability that $W\ge 2$, or equivalently the probability that $W\gt 2$, is the probability that $0$ cars go through the intersection in $2$ minutes. 
