Question

This is the random process problem.

Vehicles of two different types, cars and trucks, arrive to a gas station, so that gaps between their arrivals are independent exponential random variables with parameter 1 (vehicle per hour). Each vehicle, independently of others, is a car with probability p and is a truck with probability 1−p. Independently of other vehicles, each car and truck fills up by the number of gallons that is uniformly distributed between [8, 12] and [14, 16], respectively. In the long run, what is the average number of gallons that is sold per hour at the gas station?

Answer 1