Autore	Grimmett Geoffrey
Edizione	[Second edition.]
Pubbl/distr/stampa	Oxford, [England] : , : Oxford University Press, , 2014
Descrizione fisica	1 online resource (281 p.)
Disciplina	519.2
Soggetto topico	Probabilities
Soggetto genere / forma	Electronic books.
ISBN	9780198709978 pbk 0-19-870996-X 0-19-101992-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Cover; Preface to the second edition; Contents; Part A Basic Probability; 1 Events and probabilities; 1.1 Experiments with chance; 1.2 Outcomes and events; 1.3 Probabilities; 1.4 Probability spaces; 1.5 Discrete sample spaces; 1.6 Conditional probabilities; 1.7 Independent events; 1.8 The partition theorem; 1.9 Probability measures are continuous; 1.10 Worked problems; 1.11 Problems; 2 Discrete random variables; 2.1 Probability mass functions; 2.2 Examples; 2.3 Functions of discrete random variables; 2.4 Expectation; 2.5 Conditional expectation and the partition theorem; 2.6 Problems 3 Multivariate discrete distributions and independence3.1 Bivariate discrete distributions; 3.2 Expectation in the multivariate case; 3.3 Independence of discrete random variables; 3.4 Sums of random variables; 3.5 Indicator functions; 3.6 Problems; 4 Probability generating functions; 4.1 Generating functions; 4.2 Integer-valued random variables; 4.3 Moments; 4.4 Sums of independent random variables; 4.5 Problems; 5 Distribution functions and density functions; 5.1 Distribution functions; 5.2 Examples of distribution functions; 5.3 Continuous random variables 5.4 Some common density functions5.5 Functions of random variables; 5.6 Expectations of continuous random variables; 5.7 Geometrical probability; 5.8 Problems; Part B Further Probability; 6 Multivariate distributions and independence; 6.1 Random vectors and independence; 6.2 Joint density functions; 6.3 Marginal density functions and independence; 6.4 Sums of continuous random variables; 6.5 Changes of variables; 6.6 Conditional density functions; 6.7 Expectations of continuous random variables; 6.8 Bivariate normal distribution; 6.9 Problems; 7 Moments, and moment generating functions 7.1 A general note7.2 Moments; 7.3 Variance and covariance; 7.4 Moment generating functions; 7.5 Two inequalities; 7.6 Characteristic functions; 7.7 Problems; 8 The main limit theorems; 8.1 The law of averages; 8.2 Chebyshev's inequality and the weak law; 8.3 The central limit theorem; 8.4 Large deviations and Cram ́er's theorem; 8.5 Convergence in distribution, and characteristic functions; 8.6 Problems; Part C Random Processes; 9 Branching processes; 9.1 Random processes; 9.2 A model for population growth; 9.3 The generating-function method; 9.4 An example; 9.5 The probability of extinction 9.6 Problems10 Random walks; 10.1 One-dimensional random walks; 10.2 Transition probabilities; 10.3 Recurrence and transience of random walks; 10.4 The Gambler's Ruin Problem; 10.5 Problems; 11 Random processes in continuous time; 11.1 Life at a telephone switchboard; 11.2 Poisson processes; 11.3 Inter-arrival times and the exponential distribution; 11.4 Population growth, and the simple birth process; 11.5 Birth and death processes; 11.6 A simple queueing model; 11.7 Problems; 12 Markov chains; 12.1 The Markov property; 12.2 Transition probabilities; 12.3 Class structure 12.4 Recurrence and transience
Record Nr.	UNINA-9910460324503321