 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-iii/4/a/i/solution

p_{X, Y} (x, y) = P (X = x, Y = y), x, y \in S .

It is nonnegative and its sum over

S \times S

is one. Summing over one coordinate gives the other marginal probability mass function.

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