# Question

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.

## Answer to relevant Questions

A certain random variable has a characteristic function given by Find the PDF of this random variable. For a Poisson random variable whose PMF is given by Find the following: (a) The probability- generating function, HX( z) , (b) The Taylor series expansion of HX( z) about the point z = 1 , (c) A general expression for the ...A random variable has a moment- generating function given by (a) Find the PDF of the random variable. (b) Use the moment- generating function to find an expression for the k th moment of the random variable. Suppose X is a Gamma random variable with PDF, Find the Chernoff bound for the tail probability, Pr(X > xo). Following the lead design an optimum 2- bit quantizer for a signal whose samples follow a triangular PDF, (a) Find the four quantization levels, { y1 ,y2 ,y3 ,y4}, and the three boundary points, { x1, x2, x3}. (b) Find the ...Post your question

0