Hello, allI have pulled an all-nighter today trying to solve a take home due today at noon (EST). It's my last assignment before I graduate as a master (whatever that means). Can anyone help me answer this question for a beer (if you are located in the Northestern U.S. or London, I travel there regularly)?A Poisson process (discrete) has two devices that operate in the environment, with both devices functioning at 0. T=time to failure of device (T = h, 2h, 3h...kh)Let Ti=time to the i-th failure, i=1,2 ; assume that both devices CANNOT fail in the same interval.What is P(T2 = (k+j)h , T1 = kh) for k,j>=1Marginals of T1, T2?Distribution of (T2-T1)?Mean time before failure?thanks!

Are the two Poisson Process correlated?If not then:P(T2 = (k+j)h , T1 = kh) = P(T2 = (k+j)h)P( T1 = kh)Marginal T1, T2 = ExponetialDistribution of (T2-T1)? = Double exponential (also called Laplace)I hope this help and and congrats for your graduation! edit: just read the assumtpion that both cant fail during the same period and i dont think it holds anymore