Random variables I

Probability Examples c-2

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159 pages
In this book you find the basic mathematics that is needed by engineers and university students .
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O autorovi

Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until h

In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.

Topics as Elementary probability calculus, density functions and stochastic processes are illustrated.

This book requires knowledge of Calculus 1 and Calculus 2.

This is the second 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 topic itself, Random Variables, is so big that I have felt it necessary to divide it into three books, of which this is the first one. We shall here deal with the basic stuff, i.e. frequencies and distribution functions in 1 and 2 dimensions, functions of random variables and inequalities between random variables, as well as means and variances.

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
25th October 2009

  1. Introduction
  2. Some theoretical results
  3. Simple introducing examples
  4. Frequencies and distribution functions in 1 dimension
  5. Frequencies and distributions functions, 2 dimensions
  6. Functions of random variables, in general
  7. Inequalities between two random variables
  8. Functions Y = f(X) o f random variables
  9. Functions of two random variables, f(X; Y )
  10. Means and moments of higher order
  11. Mean and variance in special cases
  12. Index