 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/14/a/iii/solution

E [S] = \int_{0}^{1} s d s = \frac{1}{2}, E [S^{2}] = \int_{0}^{1} s^{2} d s = \frac{1}{3} .

Hence the variance is

E [S] = \frac{1}{2} minute, Var (S) = \frac{1}{3} - \frac{1}{4} = \frac{1}{12} minute^{2} .

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