Let {N(t), t 0} denote a Poisson process with rate and define Y(t) to be

Let {N(t), t ≥ 0} denote a Poisson process with rate λ and define Y(t) to be the time from t until the next Poisson event.

(a) Argue that {Y(t), t ≥ 0} is a stationary process.

(b) Compute Cov[Y(t),Y(t +s)].