 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-1/18/c/i/solution

1 = A \int_{0}^{\infty} x e^{- λ x} d x = \frac{A}{λ ^{2}} .

The integral follows from one integration by parts, with the boundary term zero since

λ > 0

. Hence $A = λ^{2}$ . This is a gamma distribution of shape

2

and rate

λ

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