Question
Let $X(t)=N(t+1)-N(t)$ where $\{N(t), t \geqslant 0\}$ is a Poisson process with rate $\lambda$. Compute$$\operatorname{Cov}[X(t), X(t+s)]$$
Step 1
We have \( X(t) = N(t+1) - N(t) \) and \( X(t+s) = N(t+s+1) - N(t+s) \). Here, \( N(t) \) is a Poisson process with rate \( \lambda \). Show more…
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