Introduction to Randomness and Statistics

TL;DR

This comprehensive introduction covers fundamental concepts of randomness, probability, data analysis, and statistical testing, with practical programming examples and tools for computer simulations and data analysis.

Contribution

It provides an accessible, self-contained overview of randomness, probability, and statistical methods with practical programming exercises and examples in C.

Findings

Explains pseudo-random number generation techniques.

Introduces bootstrap resampling and data visualization tools.

Details hypothesis testing methods like chi-squared and Kolmogorov-Smirnov.

Abstract

This text provides a practical introduction to randomness and data analysis, in particular in the context of computer simulations. At the beginning, the most basics concepts of probability are given, in particular discrete and continuous random variables. Next, generation of pseudo random numbers is covered, such as uniform generators, discrete random numbers, the inversion method, the rejection method and the Box-Mueller Method. In the third section, estimators, confidence intervals, histograms and resampling using Bootstrap are explained. Furthermore, data plotting using the freely available tools gnuplot and xmgrace is treated. In the fifth section, some foundations of hypothesis testing are given, in particular the chi-squared test, the Kolmogorov-Smirnov test and testing for statistical (in-)dependence. Finally, the maximum-likelihood principle and data fitting are explained. The text is basically self-contained, comes with several example C programs and contains eight practical (mainly programming) exercises.