| Description |
1 online resource (354 pages) |
| Series |
Chapman and Hall/CRC Texts in Statistical Science ; v. 32 |
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Chapman and Hall/CRC Texts in Statistical Science
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| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; Preface to the first edition; 1 A review of basic probability theory; 1.1 Probability and random variables; 1.2 Mean and variance; 1.3 Conditional probability and independence; 1.4 Law of total probability; 1.5 Change of variables; 1.6 Two-dimensional random variables; 1.7 Hypothesis testing â#x80;#x93; the Ï#x87;2 goodness of fit test; 1.8 Notation; References; 2 Geometric probability; 2.1 Buffonâ#x80;#x99;s needle problem; 2.2 The distance between two random points on a line segment |
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2.3 The distance between two points dropped randomly in a circle2.4 Sum of two random variables; References; Exercises; 3 Some applications of the hypergeometric and Poisson distributions; 3.1 The hypergeometric distribution; 3.2 Estimating a population from captureâ#x80;#x93;recapture data; 3.3 The Poisson distribution; 3.4 Homogeneous Poisson point process in one dimension; 3.5 Occurrence of Poisson processes in Nature; 3.6 Poisson point processes in two dimensions; 3.7 Compound Poisson random variables; 3.8 The delta function; 3.9 An application in neurobiology; References; Exercises |
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4 Reliability theory4.1 Failure time distributions; 4.2 Reliability function and failure rate function; 4.3 The spare parts problem; 4.4 Complex systems; 4.5 Series and parallel systems; 4.6 Combinations and other structures; Further reading; References; Exercises; 5 Simulation and random numbers; 5.1 The need for simulation; 5.2 The usefulness of a random sample from a uniform distribution; 5.3 Generation of uniform (0, 1) random numbers; 5.4 Generation of random numbers from a normal distribution; 5.5 Statistical tests for random numbers; 5.6 Testing for independence; References; Exercises |
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6 Convergence of sequences of random variables: the central limit theorem and the laws of large numbers6.1 Characteristic functions; 6.2 Examples; 6.3 Convergence in distribution; 6.4 The central limit theorem; 6.5 The Poisson approximation to the binomial distribution; 6.6 Convergence in probability; 6.7 Chebyshevâ#x80;#x99;s inequality; 6.8 The weak law of large numbers; References; Exercises; 7 Simple random walks; 7.1 Random processes â#x80;#x93; definitions and classifications; 7.2 Unrestricted simple random walk; 7.3 Random walk with absorbing states; 7.4 The probabilities of absorption at 0 |
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7.5 Absorption at c> 07.6 The case c = â#x88;#x9E;; 7.7 How long will absorption take?; 7.8 Smoothing the random walk â#x80;#x93; the Wiener process and Brownian motion; References; Exercises; 8 Population genetics and Markov chains; 8.1 Genes and their frequencies in populations; 8.2 The Hardy-Weinberg principle; 8.3 Random mating in finite populations: a Markov chain model; 8.4 General description of Markov chains; 8.5 Temporally homogeneous Markov chains; 8.6 Random genetic drift; 8.7 Markov chains with absorbing states; 8.8 Absorption probabilities; 8.9 The mean time to absorption; 8.10 Mutation |
| Notes |
8.11 Stationary distributions |
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Print version record |
| Subject |
Probabilities.
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probability.
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Probabilities
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| Form |
Electronic book
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| ISBN |
9781351452953 |
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1351452959 |
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