 Solution

ID: past-exam-of-the-options-i-for-mathematics-and-philosophy-course-of-the-university-of-oxford/2013/n/1/b/solution

A, B \subseteq Z

P (X \in A, Y \in B) = P (X \in A) P (Y \in B) .

p_{X, Y} (x, y) = p_{X} (x) p_{Y} (y) for every x, y \in Z .

One direction takes singleton sets; the other sums the pointwise identity over

A \times B

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