Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability / 9 / b / ii

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- Solution ii

Solution

The second moment is

E [X^{2}] = \int_{0}^{b} x^{2} \cdot a x d x = \frac{a b ^{4}}{4} = \frac{b ^{2}}{2} = \frac{9}{8} .

Subtracting the squared mean gives the variance

var (X) = \frac{9}{8} - 1^{2} = \frac{1}{8} .

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