Question: Definition and first properties of the characteristic function. Please explain as detailed as possible, thank you. 1.- Let X be the random variable with a

Definition and first properties of the characteristic function.

Please explain as detailed as possible, thank you.

1.- Let X be the random variable with a discrete distribution such that P (X = c) = 1.

a) Find the characteristic function of X.

b) If P (X = 0) = 1. Find the characteristic function of X.

2.- Let X be the random variable with binomial distribution with parameters (n, p). Find the characteristic function of X.

3.- Let X be the random variable with Poisson distribution with parameter > 0. Find the characteristic function of X.

More information in: http://www.cmat.edu.uy/~mordecki/courses/procesos-2010/Petrov-Mordecki-cap6-7.pdf

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