7-33. System failures at an industrial facility are approximately Poisson distributed with = 0.25 per hour

7-33. System failures at an industrial facility are approximately Poisson distributed with λ = 0.25 per hour (the system experiences a failure every four hours). If system startup begins at 7 A.M. on a typical work day and T is the time until the first failure occurs, find

(a) The probability that it is at least two hours until the first failure occurs

(b) The probability that it is no more than six hours until the first failure occurs

(c) The average time to the first failure

(d) The probability that the time to the next failure exceeds the average time to failure