Question: Let E|X|n < for some positive integer n. Show that the nth derivative of X(t) exists and is continuous on R, and (n) X

Let E|X|n < ∞ for some positive integer n. Show that the nth derivative of ϕX(t) exists and is continuous on R, and

ϕ(n)

X (t) ≡ dn dtn ϕX(t) = E

©

(iX)neitXª

, (2.75)

and in particular, E(Xn) =

1 in ϕ(n)

X (0). (2.76)

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