 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability/7/b/iii/solution

For

W = max {U, V}

and

0 \leq w \leq 1

F_{W} (w) = P (U \leq w, V \leq w) = w^{2} .

0

and one above

1

. Differentiating on the interior gives

f_{W} (w) = 2 w (0 < w < 1), f_{W} (w) = 0 otherwise,

up to irrelevant endpoint values. There are no endpoint atoms. This maximum is an order statistic.

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