Continuous Distributions - Probability Examples c-6

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Introduction

1 Some theoretical background
1.1 The exponential distribution
1.2 The normal distribution
1.3 2-dimensional normal distributions
1.4 Conditional normal distribution
1.5 Sums of independent normal distributed random variables
1.6 The Central Limit Theorem
1.7 The Maxwell distribution
1.8 The Gamma distribution
1.9 The 2 distribution
1.10 The t distribution
1.11 The F distribution
1.12 Estimation of parameters

2 The Exponential Distribution

3 The Normal Distribution

4 The Central Limit Theorem

5 The Maxwell distribution

6 The Gamma distribution

7 The normal distribution and the Gamma distribution

8 Convergence in distribution

9 The 2 distribution

10 The F distribution

11 The F distribution and the t distribution

12 Estimation of parameters

Index

This is the sixth book of examples from the Theory of Probability. This topic is not my favourite, however, thanks to my former colleague, Ole Jørsboe, I somehow managed to get an idea of what it is all about. The way I have treated the topic will often diverge from the more professional treatment. On the other hand, it will probably also be closer to the way of thinking which is more common among many readers, because I also had to start from scratch.

The prerequisites for the topics can e.g. be found in the Ventus: Calculus 2 series, so I shall refer the reader to these books, concerning e.g. plane integrals.

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