 Solution

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

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

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

All masses are nonnegative, and their sums over the corresponding sample values equal one.

 New to topics? Read the docs here!