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

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- Solution b

Solution

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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