A commuter attempts to catch the 8:00 am train every morningalthough his arrival time at the station is a random variable thatis uniformly distributed between 7:55 am and 8:05 am. The train's departure time from the station is also a random variable that is uniformly distributed between 8:00 am and 8:10 am.
a. Find the probability density function of the time intervalbetween the commuter's arrival at station and the train's departuretime.
b. Find the probability that the commuter will catch the train.