Assignment:
1. The random process x(t) is defined as
x(t) = Σ+∞n=-∞ rect (t-τn/T), t ε(R)
where {τn} are the ordered arrival times of a homogeneous Poisson process with rate λ = 0.8/T . Plot a realization of x(t) and find the probability P [x(t) ≤ 1].
2. Let x(t) and y(t), be two independent and homogeneous Poisson processes with rates λx = 5 . 103 s-1 and λy = 2 . 103 s-1 respectively.
a) Find mean and statistical power of the total number of arrivals for the two processes in (0, T ] with T = 3 ms.
b) Find the probability that the first arrival of y(t) proceeds the first arrival of x(t).