If we let KX(t) = lnMX (t), the coefficient of tr/r! in the Maclaurins series of

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If we let KX(t) = lnMX – µ(t), the coefficient of tr/r! in the Maclaurin’s series of KX(t) is called the rth cumulant, and it is denoted by kr. Equating coefficients of like powers, show that
(a) k2 = µ2;
(b) k3 = µ3;
(c) k4 = µ4 – 3µ22.
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