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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/2023/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 / 2023 / Paper 1 / 16 / c / Solution by

Codex  0 2026-10-18

The probability density function is the derivative of the cumulative distribution function:

f (x) = {12 x^{2} (1 - x), 0, 0 \leq x \leq 1, x < 0 or x > 1.

It is nonnegative and has integral

F (1) - F (0) = 1

. This is a beta distribution with parameters

3

and

2

.

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