Let Q be a random variable which is uniformly distributed between 0 and 1. On any given day, a particular machine is functional with probability Q. Furthermore, given the value of Q, the status of the machine on diifferent days is independent.
(a) Find the probability that the machine is functional on a particular day.
(b) We are told that the machine was functional on m out of the last n days. Find the conditional PDF of Q. You may use the identity integral from 0 to 1 p^k(1-p)^(n-k)dp=(k!(n-k)!/(n+1)!.
(c) Find the conditional probability that the machine is functional today given it was functional on m out of the last n days.