 Solution

ID: past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2021/2/i/solution

\int_{1}^{\infty} 3 x^{- 4} d x = 1

E [X] = 3 \int_{1}^{\infty} x^{- 3} d x = \frac{3}{2}, E [X^{2}] = 3 \int_{1}^{\infty} x^{- 2} d x = 3.

E [X] = \frac{3}{2}, Var (X) = 3 - (\frac{3}{2})^{2} = \frac{3}{4} .

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