A Poisson random variable has a PMF of the form (a) Find the characteristic function, Iuml X( Iuml ) (b) Find the first three nonzero terms in the Taylor series expansion of ln Iuml X( Iuml ) (c) Use the results of part (b) to find the mean, variance, and skewness of the Poisson random variable Pr(k) u exp ( a), k 0, 1, 2,

Question: A Poisson random variable has a PMF of the form (a) Find the characteristic function,ÏX( Ï ) . (b) Find the first three nonzero terms

A Poisson random variable has a PMF of the form

(a) Find the characteristic function,Ï•X( Ï‰ ) .
(b) Find the first three nonzero terms in the Taylor series expansion of ln[Ï•X(Ï‰)].
(c) Use the results of part (b) to find the mean, variance, and skewness of the Poisson random variable.

Pr(k) = u exp (-a), k = 0, 1, 2,

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