Get High-quality written work Help from our Professionals answer 6 questionsfinish in Get High-quality written work Help from our Professionals hour of the file. Get High-quality written work Help from our Professionals . A technology company has two independent servers. Denote X as the downtime in hours of server Get High-quality written work Help from our Professionals and denote Y as the downtime in hours of server 2. X follows an exponential distribution with parameter β > 0 and Y follows an exponential distribution with parameter α > 0 where β and α are both finite. Assume X and Y are independent of one another.a. What is the probability that server Get High-quality written work Help from our Professionals will be down at least as long as server 2 is down? Show work.b. What is E[X(X + Y )] and var(X + Y )? Show work and reasoning. c. Derive the moment generating function for server Get High-quality written work Help from our Professionals ’s downtime (X) and use it to get the third moment of X (that is get E(X3)). Show work. d. Derive the moment generating function for the combined down time across server Get High-quality written work Help from our Professionals and server 2 X +Y. Show work. e. Now say we have a sequence of n many servers such that the downtime on server n Xn follows an exponential distribution with parameter n.Show that Xn converges in probability to 0 as n goes to infinity.