Tyree enters the bus stop at 10 AM in Prospect Ave at Park Slope, Brook-lyn.The"waiting time"forthebusisarandomvariablethatsatisfies roughly the exponential distribution(see below for details).If there is anaccident in the Prospect Ave, the average waiting time for the bus is 40minutes.If there is no accident, the average waiting time is 10 minutes. Ordinarily, there is a 7% chance of an accident in the Prospect Ave around this time of the day. Tyree waited 25 minutes until the bus showed up.What is the probability that an accident happened? TheExponentialDistribution isacontinuousdistributionwhichis often used to model waiting time for some events. It has one parameter which is the average waiting time. Herearesomeusefulinformation about this distribution:

pdf:fX(t) =1exp(t)

CDF:FX(t) =1exp(t)

Expected value:EX=

Variance:Var(X) =2

Carefully pose the question in terms of conditional distribution and show how you find the solution.

Search R to learn how to conduct calculations regarding the exponential distribution.