Let x be the interarrival time between consecutive events specified by the probability density function fx(x0) = 27 2 x 3 0 e 3x0 , x0 0. Interarrival times are independent. a. (5pts)Find the expected value of the interarrival time y between the 10th and the 13th events. b. (10pts)Find the probability density function for the interarrival time z between the 12th and 18th events. c. (10pts)If we arrive at the process at a random time, determine the probability density function for the total length of the interarrival gap which we shall enter. d. (10pts)Determine the expected value and the variance of random variable defined by = 2y + 3z.

Let o be the interarrival time between consecutive events specified by the proba- bility density function 27 fe(10) = 25e-360, 20 > 0. Interarrival times are independent. a. (5pts)Find the expected value of the interarrival time y between the 10th and the 13th events. b. (10pts)Find the probability density function for the interarrival time z between the 12th and 18th events. c. (10pts)If we arrive at the process at a random time, determine the probability density function for the total length of the interarrival gap which we shall enter. d. (10pts)Determine the expected value and the variance of random variables defined by 5 = 2y + 3z. Let o be the interarrival time between consecutive events specified by the proba- bility density function 27 fe(10) = 25e-360, 20 > 0. Interarrival times are independent. a. (5pts)Find the expected value of the interarrival time y between the 10th and the 13th events. b. (10pts)Find the probability density function for the interarrival time z between the 12th and 18th events. c. (10pts)If we arrive at the process at a random time, determine the probability density function for the total length of the interarrival gap which we shall enter. d. (10pts)Determine the expected value and the variance of random variables defined by 5 = 2y + 3z