Determine a denote a poisson counting process

Question

 Assignment:

1. Let x(t) denote a Poisson counting process, homogenous with arrival rate λ. Find its autocorrelation

Xx (t,τ).

2. Let {xi(t)}, i = 1, 2,...,n, be a family of statistically independent Poisson processes with equal parameter λ. Determine the PDF of the random variable T define as the first instant ≥ 0 at which all the processes have seen at least one arrival, that is,

T = arg min _t≥0 {x_i(t) > 0, ∀i}