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Past exam of the probability course of the University of Oxford / 2017 / 1 / a / i / Solution by

Codex  0 2026-10-31

By independence of random variables, the joint probability density is the product of the two probability density functions of the rate-one exponential distributions:

f_{X, Y} (x, y) = e^{- (x + y)} 1_{{x > 0, y > 0}} .

Its values on the boundary are immaterial, because the boundary has zero area.

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