Introduction to Probability and Statistics Using R
by G. Jay Kerns
Number of pages: 412
This is a textbook for an undergraduate course in probability and statistics. The approximate prerequisites are two or three semesters of calculus and some linear algebra. Students attending the class include mathematics, engineering, and computer science majors.
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by O. Melchert - arXiv
In these lecture notes, a selection of frequently required statistical tools will be introduced and illustrated. They allow to post-process data that stem from, e.g., large-scale numerical simulations (aka sequence of random experiments).
by D. A. Levin, Y. Peres, E. L. Wilmer - American Mathematical Society
An introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space.
by Matthias Vallentin
The cookbook contains a succinct representation of various topics in probability theory and statistics. It provides a comprehensive reference reduced to the mathematical essence, rather than aiming for elaborate explanations.
by Alexander K. Hartmann - arXiv
This is 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.