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) lnMX (t), the coefficient of tr r in the Maclaurins series of KX(t) is called the rth cumulant, and it is denoted by kr Equating coefficients of like powers, show th...

With reference to Exercise 6.39, show that for normal distributions k2= 2 and all other cumulants are

Question:

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