 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2019/discrete-mathematics-continuous-mathematics-and-probability-resit/8/a/i/solution

For an integrable discrete random variable, the conditional expectation given an event

B

of positive probability is

E [X ∣ B] = x \sum x P (X = x ∣ B) = x \sum x \frac{P ({ X = x } \cap B )}{P ( B )} .

The sum ranges over the possible values of

X

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