With reference to exercise 39 show that for normal, Ask an Expert

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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

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