Paul Gerhard Hoel (1905–2000)

Indeholder "Preface", "General preface", "1. Probability Spaces ", "1.1 Examples of random phenomena", "1.2 Probability spaces", "1.3 Properties of probabilities", "1.4 Conditional probability", "1.5 Independence ", "2. Combinatorial Analysis", "2.1 Ordered samples", "2.2 Permutations", "2.3 Combinations (unordered samples)", "2.4 Partitions", "2.5 Union of events", "2.6 Matching problems", "2.7 Occupancy problems", "2.8 Number of empty boxes", "3 Discrete Random Variables", "3.1 Definitions", "3.2 Computations with densities", "3.3 Discrete random vectors", "3.4 Independent random variables", "3.4.1 The multinomial distribution", "3.4.2 Poisson approximation to the binomial distribution", "3.5 Infinite sequences of Bernoulli trials", "3.6 Sums of independent random variables", "4 Expectation of Discrete Random Variables", "4.1 Definition of expectation", "4.2 Properties of expectation", "4.3 Moments", "4.4 Variance of a sum", "4.5 Correlation coefficient", "4.6 Chebyshev's Inequality", "5 Continuous Random Variables", "5.1 Random variables and their distribution functions", "5.1.1 Properties of distribution functions", "5.2 Densities of continuous random variables", "5.2.1 Change of variable formulas", "5.2.2 Symmetric densities", "5.3 Normal, exponential, and gamma densities", "5.3.1 Normal densities", "5.3.2 Exponential densities", "5.3.3 Gamma densities", "5.4 Inverse distribution functions", "6 Jointly Distributed Random Variables", "6.1 Properties of bivariate distributions", "6.2 Distribution of sums and quotients", "6.2.1 Distribution of sums", "6.2.2 Distribution of quotients", "6.3 Conditional densities", "6.3.1 Bayes' rule", "6.4 Properties of multivariate distributions", "6.5 Order statistics", "6.6 Sampling distributions", "6.7 Multidimensional changes of variables", "7 Expectations and the Central Limit Theorem", "7.1 Expectations of continuous random variables", "7.2 A general definition of expectation", "7.3 Moments of continuous random variables", "7.4 Conditional expectation", "7.5 The Central Limit Theorem", "7.5.1 Normal approximations", "7.5.2 Applications to sampling", "8 Moment Generating Functions and Characteristic Functions", "8.1 Moment generating functions", "8.2 Characteristic functions", "8.3 Inversion formulas and the Continuity Theorem", "8.4 The Weak Law of Large Numbers and the Central Limit Theorem", "9 Random Walks and Poisson Processes", "9.1 Random walks", "9.2 Simple random walks", "9.3 Construction of a Poisson process", "9.4 Distance to particles", "9.5 Waiting times", "Answers to Exercises", "Table I", "Index".

Udmærket introduktion til sandsynlighedsteori. Bogen er den første af tre lærebøger, hvor de andre to er om statistik og om stokastiske processer.
Bogens eksempler er fine og der er en facitliste til alle øvelserne bagerst.… (mehr)