 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/discrete-mathematics-continuous-mathematics-and-probability/9/a/iv/solution

The conditional mean of a Poisson distribution equals its parameter, so

E [Z ∣ X] = X

E Z = E X = μ .

As a check, differentiating the probability generating function in part (iii) at one also gives

G_{Z}^{'} (1) = μ

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