With reference to Exercise 6.39, show that for normal distributions k2= 2 and all other cumulants are zero. In exercise If we let KX(t) =

With reference to Exercise 6.39, show that for nor–mal distributions k2= σ2 and all other cumulants are zero.
In exercise
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