 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/9/b/ii/solution

E (Y) = \int_{0}^{\infty} xg (x) d x = \frac{1}{μ} \int_{0}^{\infty} x^{2} f (x) d x = \frac{E ( X ^{2} )}{μ} = μ + \frac{σ ^{2}}{μ} .

Thus size bias increases the mean by

σ^{2} / μ

, in accord with preferentially selecting larger values.

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