Problem 6. A Poisson process with an average arrival rate of B arrivals per hour begins at time 0. Immediately after each arrival, the average arrival rate for the process is doubled. Define X as the time at which the first arrival occurs, Y as time at which the second arrival occurs, and Z as the time at which the third arrival occurs. a) Determine the expectation, variance and third moment of variable K = Z - X b) Determine either the PDF or the transform for K + Y c) Find P(A), where A is the event that the time between the first and third arrivals is greater than the time from 0 until the second arrival