1. By making use of the independence and homogeneity of the increments of a homogeneous Poisson process {N(t), t ≥ 0} with intensity λ show that its covariance function is given by 2. Let {N(t), t ≥...

1. By making use of the independence and homogeneity of the increments of a homogeneous Poisson process {N(t), t ≥ 0} with intensity λ show that its covariance function is given by

2. Let {N(t), t ≥ 0} be a homogeneous Poisson process with intensity λ. Prove that for an arbitrary, but fixed positive h the stochastic process {X(t), t ≥ 0} defined by

is weakly stationary.