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Covariance of a Poisson process

MediumStochastic Processes~4m

Let N(t)N(t) be a Poisson process with rate 55. Compute Cov⁡(N(5),N(15))\operatorname{Cov}\big(N(5), N(15)\big).

Show hints (2)+
  1. N(15)=N(5)+[N(15)−N(5)]N(15)=N(5)+[N(15)-N(5)], and the increment is independent of N(5)N(5).
  2. So the covariance is Var⁡(N(5))=λ⋅5=25\operatorname{Var}(N(5))=\lambda\cdot5=25.

Answer

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25

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Asked at: Citadel, Two Sigma

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