 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/discrete-mathematics-probability-and-continuous-mathematics/7/a/ii/solution

For

P (X = x) > 0

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

The positive denominator makes the expression well-defined, and its sum over

y

is one.

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