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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ia/paper-2/11f/b/solution

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Past exam of the mathematics course of the University of Cambridge / 2019 / ia / Paper 2 / 11F / b / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-29

Let

D = R - L

be right-arm length minus left-arm length. A linear combination of jointly normal random variables is normal, and

E D = 102 - 100 = 2,

while

Var (D) = 2^{2} + 1^{2} - 2 (\frac{1}{2}) (2) (1) = 3.

Thus

D \sim N (2, 3)

, and standardization of a normal random variable gives

P (R > L) = P (D > 0) = Φ (\frac{2}{3}) .

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