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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/2016/paper-2/16/a/ii/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 / 2016 / Paper 2 / 16 / a / ii / Solution by

Codex  0 2026-10-18

Compute the first two moments from the probability distribution:

μ = E [X] = \frac{6}{10} + \frac{6}{10} = \frac{6}{5}, E [X^{2}] = \frac{6}{10} + \frac{12}{10} = \frac{9}{5} .

The variance is

E [X^{2}] - E [X]^{2} = 9/5 - 36/25 = 9/25

, so the expected value and standard deviation are

μ = \frac{6}{5}, σ = \frac{3}{5} .

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