Radically Elementary Probability Theory
by Edward Nelson
Publisher: Princeton University Press 1987
Number of pages: 111
Nelson develops a new approach to probability theory that is just as powerful as but much simpler than conventional Kolmogorov-style probability theory used throughout mathematics for most of the 20th century.
Home page url
Download or read it online for free here:
by Leif Mejlbro - BookBoon
From the table of contents: Some theoretical background; The binomial distribution; The Poisson distribution; The geometric distribution; The Pascal distribution; The negative binomial distribution; The hypergeometric distribution.
by H.R. Pitt - Tata institute of Fundamental Research
Measure Theory (Sets and operations on sets, Classical Lebesgue and Stieltjes measures, Lebesgue integral); Probability (Function of a random variable, Conditional probabilities, Central Limit Problem, Random Sequences and Convergence Properties).
by Douglas Kennedy - Trinity College
This material was made available for the course Probability of the Mathematical Tripos. Contents: Basic Concepts; Axiomatic Probability; Discrete Random Variables; Continuous Random Variables; Inequalities, Limit Theorems and Geometric Probability.
by Cosma Rohilla Shalizi - Carnegie Mellon University
Text for a second course in stochastic processes. It is assumed that you have had a first course on stochastic processes, using elementary probability theory. You will study stochastic processes within the framework of measure-theoretic probability.