A first course in probability / Sheldon M Ross.

Includes index.

combinatorial analysis -- 1.1 introduction -- 1.2 the basic principle of counting -- 1.3 permutations -- 1.4 combinations -- 1.5 multinomial coefficients -- 1.6 on the distribution of balls in urns* -- summary -- problems -- theoretical exercises -- self-test problems and exercises -- 2 axioms of probability -- 2.1 introduction -- 2.2 sample space and events -- 2.3 axioms of probability -- 2.4 some simple propositions -- 2.5 sample spaces having equally likely outcomes -- 2.6 probability as a continuous set function* -- 2.7 probability as a measure of belief -- summary -- problems -- theoretical exercises -- self-test problems and exercises -- 3 conditional probability and independence -- 3.1 introduction -- 3.2 conditional probabilities -- 3.3 bayes' formula -- 3.4 independent events -- 3.5 p(.\f) is a probability(*) -- summary -- problems -- theoretical exercises -- self-test problems and exercises -- 4 random variables -- 4.1 random variables -- 4.2 distribution functions -- 4.3 discrete random variables -- 4.4 expected value -- 4.5 expectation of a function of a random variable -- 4.6 variance -- 4.7 the bernoulli and binomial random variables -- 4.7.1 properties of binomial random variables -- 4.7.2 computing the binomial distribution function -- 4.8 the poisson random variable -- 4.8.1 computing the poisson distribution function -- 4.9 other discrete probability distribution -- 4.9.1 the geometric random variable -- 4.9.2 the negative binomial random variable -- 4.9.3 the hypergeometric random variable -- 4.9.4 the zeta (or zipf) distribution -- summary -- problems -- theoretical exercises -- self-test problems and exercises -- 5 continuous random variables -- 5.1 introduction -- 5.2 expectation and variance of continuous random variables -- 5.3 the uniform random variable -- 5.4 normal random variables -- 5.4.1 the normal approximation to the binomial distribution -- 5.5 exponential random variables -- 5.5.1 hazard rate functions -- 5.6 other continuous distributions -- 5.6.1 the gamma distribution -- 5.6.2 the weibull distribution -- 5.6.3 the cauchy distribution -- 5.6.4 the beta distribution -- 5.7 the distribution of a function of a random variable -- summary -- problems -- theoretical exercises -- self-test problems and exercises -- 6 jointly distributed random variables -- 6.1 joint distribution functions -- 6.2 independent random variables -- 6.3 sums of independent random variables -- 6.4 conditional distributions: discrete case -- 6.5 conditional distributions: continuous case -- 6.6 order statistics* -- 6.7 joint probability distribution of functions of random variables -- 6.8 exchangeable random variables* -- summary -- problems -- theoretical exercises -- self-test problem and exercises -- 7 properties of expectation -- 7.1 introduction -- 7.2 expectation of sums of random variables -- 7.3 covariance, variance of sums, and correlations -- 7.4 conditional expectation -- 7.4.1 definitions -- 7.4.2 computing expectations by conditioning -- 7.4.3 computing probabilities by conditioning -- 7.4.4 conditional variance -- 7.5 conditional expectation and prediction -- 7.6 moment generating functions -- 7.6.1 joint moment generating functions -- 7.7 additional properties of normal random variables -- 7.7.1 the multivariate normal distribution -- 7.7.2 the joint distribution of the sample mean and sample variance -- 7.8 general definition of expectation(*) -- summary -- problems -- theoretical exercises -- self-test problems and exercises -- 8 limit theorems -- 8.1 introduction -- 8.2 chebyshev's inequality and the weak law of large numbers -- 8.3 the central limit theorem -- 8.4 the strong law of large numbers -- 8.5 other inequalities -- 8.6 bounding the error probability when approximating a sum of independent bernoulli random variables by a poisson -- summary -- problems -- theoretical exercises -- self-test problems and exercises -- 9 additional topics in probability -- 9.1 the poisson process -- 9.2 markov chains -- 9.3 surprise, uncertainty, and entropy -- 9.4 coding theory and entropy -- summary -- theoretical exercises and problems -- self-test problems and exercises -- references -- 10 simulation -- 10.1 introduction -- 10.2 general techniques for simulating continuous random variables -- 10.2.1 the inverse transformation method -- 10.2.2 the rejection method -- 10.3 simulating from discrete distributions -- 10.4 variance reduction techniques -- 10.4.1 use of antithetic variables -- 10.4.2 variance reduction by conditioning -- 10.4.3 control variates -- summary -- problems -- self-test problems and exercises -- references -- appendix a answers to selected problems -- appendix b solutions to self-test problems and exercise -- index.

This market leader is written as an elementary introduction to the mathematical theory of probability for students in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's students. The exercise sets have been revised to include more simple, mechanical problems and a new section of Self-Test Problems with fully worked out solutions conclude each chapter. In addition, many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, referenced in text and packaged with each copy of the book, provides an easy to use tool for students to derive probabilities for binomial, Poisson, and normal random variables, illustrate and explore the central limit theorem, work with the strong law of large numbers, and more.