 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ia/paper-2/4f/b/solution

With

μ = E X

Var X = \sum_{x} P (X = x) (x - μ)^{2} .

Every summand is nonnegative. If the sum is zero, every value of positive probability equals

μ

, so $P (X = μ) = 1$ .

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