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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/16/c/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 1 / 16 / c / Solution by

Codex  0 2026-10-18

Since the probability density function is an even function,

x f (x)

is an odd function. Its integral over the symmetric support vanishes, so

E [X] = 0.

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