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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/i/solution

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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 / i / Solution by

Codex  0 2026-10-25

By independence, the joint probability density is the product of the two uniform distribution densities:

f_{U, V} (u, v) = 1_{{0 \leq u \leq 1, 0 \leq v \leq 1}} .

Changing its values on the boundary does not affect any probability or expected value.

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