With reference to exercise 39 show that for normal

Question

With reference to Exercise 39, show that for normal distributions κ₂ =σ² and all other cumulants are zero.

Exercise 39

If we let

 in the Maclaurin's series of K_X(t) is called the rth cumulant, and it is denoted by κ_r. Equating coefficients of like powers, show that