Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability / 9 / a / iii

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- Solution iii

Solution

Use the covariance identity and the moments from (ii):

Cov (X, X^{2}) = E (X^{3}) - E (X) E (X^{2}) = \frac{1}{4} - \frac{1}{2} \cdot \frac{1}{3} = \frac{1}{12} .

The positive value is consistent with both

X

and

X^{2}

increasing together on

[0, 1]

.

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