 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-2/10/b/solution

E [X] = \frac{1}{2} \int_{0}^{π} x sin x d x = \frac{1}{2} [- x cos x + sin x]_{0}^{π} = \frac{π}{2} .

The same result follows from symmetry of the probability density function about

π /2

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