Covariance of a Poisson process

MediumStochastic Processes~4m

Let $N(t)$ be a Poisson process with rate $5$ . Compute $\operatorname{Cov}\big(N(5), N(15)\big)$ .

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$N(15)=N(5)+[N(15)-N(5)]$ , and the increment is independent of $N(5)$ .
So the covariance is $\operatorname{Var}(N(5))=\lambda\cdot5=25$ .

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25

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