A Modern Introduction to Probability and Statistics

Probability and statistics are fascinating subjects on the interface between

mathematics and applied sciences that help us understand and solve practical

problems. We believe that you, by learning how stochastic methods come

about and why they work, will be able to understand the meaning of statistical

statements as well as judge the quality of their content, when facing such

problems on your own. Our philosophy is one of how and why: instead of just

presenting stochastic methods as cookbook recipes, we prefer to explain the

principles behind them.

In this book you will find the basics of probability theory and statistics. In

addition, there are several topics that go somewhat beyond the basics but

that ought to be present in an introductory course: simulation, the Poisson process, the law of large numbers, and the central limit theorem.