A Natural Introduction to Probability Theory

This introduction to probability theory is an excellent textbook for a one-semester course for undergraduates in any direction that uses probabilistic ideas. Compact but readable, it appeals to intuition and introduces technical machinery only when necessary.

Compactly written, but nevertheless very readable, appealing to intuition, this introduction to probability theory is an excellent textbook for a one-semester course for undergraduates in any direction that uses probabilistic ideas. Technical machinery is only introduced when necessary.

The route is rigorous but does not use measure theory. The text is illustrated with many original and surprising examples and problems taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports, and coding theory. Only first-year calculus is required.

Discovering of the theory along the way, rather than presenting it matter of factly at the beginning Contains many original and surprising examples A rigorous study without any measure theory Compactly written, but nevertheless very readable A probabilistic approach, appealing to intuition, introducing technical machinery only when necessary Includes supplementary material: sn.pub/extras

Inhalt
Experiments.- Random Variables and Random Vectors.- Random Walk.- Limit Theorems.- Intermezzo.- Continuous Random Variables and Vectors.- Infinitely Many Repetitions.- The Poisson Process.- Limit Theorems.- Extending the Probabilities.