Probability Theory and Statistical Applications

This accessible and easy-to-read book provides many examples to illustrate diverse topics in probability and statistics, from initial concepts up to advanced calculations. Special attention is devoted e.g. to independency of events, inequalities in probability and functions of random variables. The book is directed to students of mathematics, statistics, engineering, and other quantitative sciences, in particular to readers who need or want to learn by self-study. The author is convinced that sophisticated examples are more useful for the student than a lengthy formalism treating the greatest possible generality.

Contents:

Mathematics revision

Introduction to probability

Finite sample spaces

Conditional probability and independence

One-dimensional random variables

Functions of random variables

Bi-dimensional random variables

Characteristics of random variables

Discrete probability models

Continuous probability models

Generating functions in probability

Sums of many random variables

Samples and sampling distributions

Estimation of parameters

Hypothesis tests