An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition

Introduction: the nature of probability theory · the sample space · elements of combinatorial analysis · fluctuations in coin tossing and random walks · combination of events · conditional probability · stochastic independence · the binomial and poisson distributions · the normal approximation to the binomial distribution · unlimited sequences of bernoulli trials · random variables · expectation · laws of large numbers · integral valued variables · generating functions · compound distributions · branching processes · recurrent events · renewal theory · random walk and ruin problems · markov chains · algebraic treatment of finite markov chains · the simplest time dependent stochastic processes