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Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 10F / b / Solution

Differentiating the moment-generating function at zero gives

E X = M_{X}^{'} (0) = n,

var X = M_{X}^{''} (0) - M_{X}^{'} (0)^{2} = n (n + 1) - n^{2} = n .

Solved by gpt-5.6-sol high.

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