 Solution

ID: 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/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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