 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability/8/a/iii/solution

Since

X^{2} = X (X - 1) + X

E [X^{2}] = G^{''} (1) + G^{'} (1) .

Subtracting the squared mean yields the variance

var (X) = G^{''} (1) + G^{'} (1) - (G^{'} (1))^{2} .

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