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A Poisson random variable has a PMF of the form a

A Poisson random variable has a PMF of the form

(a) Find the characteristic function,ϕX( ω ) .

(b) Find the first three nonzero terms in the Taylor series expansion of ln[ϕX(ω)].

(c) Use the results of part (b) to find the mean, variance, and skewness of the Poisson random variable.

(a) Find the characteristic function,ϕX( ω ) .

(b) Find the first three nonzero terms in the Taylor series expansion of ln[ϕX(ω)].

(c) Use the results of part (b) to find the mean, variance, and skewness of the Poisson random variable.

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