 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/9/a/i/solution

\int_{- \infty}^{\infty} f (x) d x = α \int_{0}^{2} x^{2} d x = \frac{8 α}{3} .

Therefore

α = \frac{3}{8}, f is a valid density .

This value is positive, so the nonnegativity requirement also holds.

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