 Solution

ID: past-exam-of-the-options-ii-course-of-the-university-of-oxford/2012/m/m5/d/solution

Write

N_{3} = N_{2} + (N_{3} - N_{2})

N_{2}

independent of the second term. Hence

Cov (N_{2}, N_{3}) = Var (N_{2}) = 2 λ .

The overlapping time interval contributes the covariance; the extra unit of time contributes none.

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