 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2001/paper-1/12/a/solution

P

, the mean and variance are

μ = \int_{- \infty}^{\infty} x P (x) d x, σ^{2} = \int_{- \infty}^{\infty} (x - μ)^{2} P (x) d x = E [X^{2}] - μ^{2} .

These formulas assume the required moments are finite; finiteness of the second moment ensures a finite mean as well.

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