Textbook in PDF and DJVU formats

Preface Set Sample sets Operations with sets Various relations Indicator Exercises Probability Examples of probability Definition and illustrations Deductions from the axioms Independent events Arithmetical density Exercises Counting Fundamental rule Diverse ways of sampling Allocation models; binomial coefficients How to solve it Exercises Random Variables What is a random variable? How do random variables come about? Distribution and expectation Integer-valued random variables Random variables with densities General case Exercises Borel Fields and General Random Variables Conditioning and Independence Examples of conditioning Basic formulas Sequential sampling Pólya's urn scheme Independence and relevance Genetical models Exercises Mean, Variance and Transforms Basic properties of expectation The density case Multiplication theorem; variance and covariance Multinomial distribution Generating function and the like Exercises Poisson and Normal Distributions Models for Poisson distribution Poisson process From binomial to normal Normal distribution Central limit theorem Law of large numbers Exercises Stirling's Formula and De Moivre-Laplace's Theorem From Random Walks to Markov Chains Problems of the wanderer or gambler Limiting schemes Transition probabilities Basic structure of Markov chains Further developments Steady state Winding up (or down?) Exercises Martingale General References Answers to Problems Table Values of the standard normal distribution function Index