Problem 3: Generalizing problem 2. Suppose that the distribution of bus headways is given by fH(h). Also assume that passengers arrive at a rate of per unit time. a) Following the logic of problem 2, given that the headway is h, what is the average waiting time of a passenger who arrives during that headway? b) Following the logic of problem 2, given that the headway is h, what is the average number of passengers who arrive during that headway? c) Now, find the expected number of passengers to arrive during any headway. We need to just take the value of part (b) and multiply by fH(h) and then integrate over all values of the headway. Simplify as much as possible. d) Following the logic of problem 2, given that the headway is h, what is the average number of passenger minutes of waiting time that accumulate during that headway? e) Now find the expected number of passenger minutes during any headway. . We need to just take the value of part (d) and multiply by fH(h) and then integrate over all values of the headway. Simplify as much as possible. f) Now find the average waiting time which should be part (e) divided by part (c). g) If you did part (f) correctly, it should depend on E(H2). Rewrite the equation in part (f) so that it depends on E(H) and Var(H)