 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability-resit/7/a/i/solution

For a nonnegative integer-valued random variable, its expectation is the probability-weighted sum

E (X) = j = 0 \sum \infty j P (X = j) .

All terms are nonnegative, so this is always defined as an extended nonnegative number, possibly

+ \infty

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