Let x(t) be a Poisson process with rate and fix instants t 1 = 0 ms, t 2 = 3 ms, t 3 = 4 ms, t 4 =…

Let x(t) be a Poisson process with rate  and fix instants t1 = 0 ms, t2 = 3 ms, t3 = 4 ms, t4 = 5 ms
a) Find the probability that exactly 2 arrivals lie in the interval (t2, t4), given that there are none in the interval (t1, t3).
b) Let  be two unordered arrivals in the interval (t3, t4), find the mean and variance of their difference