Calculating Moment Generating and Characteristic Functions Using Mathematica

Fu-Chuen Chang ； Jeff Shao

《中國統計學報》 46卷2期 (2008/06) Pp. 118-129

https://doi.org/10.29973/JCSA.200806.0003

並列摘要

In this paper, we define some functions to extend Mathematica's capabilities to handle symbolic computations of the moment generating function and characteristic function for linear combination of independent random variables. These functions utilizes pattern-matching codes that enhance Mathematica's ability to simplify expressions involving the product of algebraic terms. Several examples will be presented. The examples include using Mathematica for calculating mean and variance, determining the distribution of sum of independent random variables and illustrating the central limit theorem and the law of large numbers.

並列關鍵字

Characteristic function ； computer algebra system ； central limit theorem ； law of large numbers ； Mathematica ； moment generating function ； teaching probability

參考文獻

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Grimmett, G.,Welsh, D.(1986).Probability: An Introduction.New York:Oxford University Press.

Wolfram, S.(2003).The Mathematica Book, 5th edition.Wolfram Media:Champaign, IL.