Analytic Aids - Probability Examples c-7

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Introduction

1 Generating functions; background
1.1 Denition of the generating function of a discrete random variable
1.2 Some generating functions of random variables
1.3 Computation of moments
1.4 Distribution of sums of mutually independent random variables
1.5 Computation of probabilities
1.6 Convergence in distribution

2 The Laplace transformation; background
2.1 Denition of the Laplace transformation
2.2 Some Laplace transforms of random variables
2.3 Computation of moments
2.4 Distribution of sums of mutually independent random variables
2.5 Convergence in distribution

3 Characteristic functions; background
3.1 Denition of characteristic functions
3.2 Characteristic functions for some random variables
3.3 Computation of moments
3.4 Distribution of sums of mutually independent random variables
3.5 Convergence in distribution

4 Generating functions

5 The Laplace transformation

6 The characteristic function

Index

This is the eight book of examples from the Theory of Probability. In general, this topic is not my favourite, but thanks to my former colleague, Ole Jørsboe, I somehow managed to get an idea of what it is all about. We shall, however, in this volume deal with some topics which are closer to my own mathematical fields.

The prerequisites for the topics can e.g. be found in the Ventus: Calculus 2 series and the Ventus: Complex Function Theory series, and all the previous Ventus: Probability c1-c6.

Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors which do occur in the text.

Leif Mejlbro
27th October 2009