Starting at some fixed time, which we will call 0 for convenience, satellites are launched at times of a poisson process with rate λ. after an independent amount of time having distribution function f and mean µ, the satellite stops working. let x(t) be the number of working satellites at time t. (a) find the distribution of x(t). (b) let t → [infinity] in (a) to show that the limiting distribution is poisson(λµ).