Probability / Peter Whittle

Por: Whittle, Peter, 1927-Series Library of university mathematics; Penguin educationEditor: Harmondsworth, Penguin, 1970Descripción: 3-239 p. illus. 21 cmISBN: 0140800859Tema(s): ProbabilitiesOtra clasificación: *CODIGO*
Contenidos:
Preface --
1 Introduction [15] --
1.1 A few ideasand examples [15] --
1.2 The empirical basis [16] --
1.3 Averages over a finite population [19] --
1.4 Repeated experiments; expectation [21] --
1.5 More on sample spaces and observables [22] --
2 Expectation [25] --
2.1 Random variables [25] --
2.2 Axioms for the expectation operator [26] --
2.3 Events; probability [28] --
2.4 Some examples of an expectation [29] --
2.5 Applications: optimization problems [33] --
2.6 Applications: least square approximation of random variables [35] --
2.7 Some implications of the axioms [38] --
3 Probability [43] --
3.1 Probability measure [43] --
3.2 Probability and expectation [45] --
3.3 Expectation as an integral [48] --
3.4 Elementary properties of events and probabilities [50] --
3.5 Fields of events [53] --
4 Some Simple Processes [56] --
4.1 Equiprobable sample spaces [56] --
4.2 A coin-tossing example; stochastic convergence [57] --
4. 3 A more general example; the binomial distribution [60] --
4.4 Multiple classification; the multinomial distribution [63] --
4.5 Sampling without replacement; the hypergeometric distribution [65] --
4.6 Indefinite sampling; the geometric and negative binomial distributions [68] --
4.7 Sampling from a continuum: the Poisson process [71] --
4.8 'Nearest neighbours'; the exponential and gamma distributions [73] --
4.9 Other simple processes [74] --
5 Conditioning [80] --
5.1 Conditional expectation [80] --
5.2 Conditional probability [84] --
5.3 A conditional expectat ion as a random v aria ble [88] --
5.4 4 Conditioning on a a-field of events [90] --
5.5 Statistical independence [93] --
5.6 Elementary consequences of independence [95] --
5.7 Partial independence ; orthogonality [101] --
6 Applications of the Independence Concept [104] --
6.1 Mean square convergence of sample average [104] --
6.2 Convergence of sample average*. some slrongrr result [106] --
6.3 Renewal processes [109] --
6.4 Recurrent slates (events) [113] --
6.5 A result in statistical mechanics [117] --
6.6 Branching processes [120] --
7 Markov Processes [128] --
7.1 The Markov propery [121] --
7.2 Some particular Markov processes [133] --
7.3 The simple randmon walk [37] --
7.4 Markov processes in continuous time [139] --
7.5 The Poisson processes in time [141] --
7.6 Birth processes [144] --
7.7 Birth and death processes. [147] --
8 Continuous Distributions [150] --
8.1 Distributions whith a density [150] --
8.2 Functions of randmon variables [153] --
8.3 Conditional densities [159] --
8.4 Characteristic functions [161] --
8.5 The normal distribution; normal convergence [167] --
8.6 A direct proof of norma convergence [171] --
9 Convergence of Randmon Sequences 174 9.1 Characterizacion of convergence [174] --
9.2 Types of convergence [176] --
9.3 Some consequences [178] --
9.4 Kolmogorov´s inequality, and refenements of it [180] --
9.5 The laws of large numbers [183] --
9.6 Martingale convergence, and applications [186] --
9.7 Convergence in rth mean [189] --
10 Extension [194] --
10.1 Extension of the expectation functional :he finite case [194] --
10.2 Generalities on the infinite case [197] --
10.3 Extension on a linear lattice [199] --
10.4 Extension on a quadratic field [201] --
11 Examples of Extension [204] --
11.1 Integrable functions of a scalar random variable [204] --
11.2 Expectations derivable from the characteristic function [206] --
12 Some Interesting Processes [212] --
12.1 Quantum mechanics [212] --
12.2 Information theory [218] --
12.3 Dynamic programming; stock control [223] --
12.4 Stochastic differential equations: generalized processes [227] --
References [233] --
Index [235] --
List(s) this item appears in: Últimas adquisiciones
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Últimas adquisiciones 60 W627 (Browse shelf) Available A-9351

Bibliografía: p. 233.

Preface --
1 Introduction [15] --
1.1 A few ideasand examples [15] --
1.2 The empirical basis [16] --
1.3 Averages over a finite population [19] --
1.4 Repeated experiments; expectation [21] --
1.5 More on sample spaces and observables [22] --
2 Expectation [25] --
2.1 Random variables [25] --
2.2 Axioms for the expectation operator [26] --
2.3 Events; probability [28] --
2.4 Some examples of an expectation [29] --
2.5 Applications: optimization problems [33] --
2.6 Applications: least square approximation of random variables [35] --
2.7 Some implications of the axioms [38] --
3 Probability [43] --
3.1 Probability measure [43] --
3.2 Probability and expectation [45] --
3.3 Expectation as an integral [48] --
3.4 Elementary properties of events and probabilities [50] --
3.5 Fields of events [53] --
4 Some Simple Processes [56] --
4.1 Equiprobable sample spaces [56] --
4.2 A coin-tossing example; stochastic convergence [57] --
4. 3 A more general example; the binomial distribution [60] --
4.4 Multiple classification; the multinomial distribution [63] --
4.5 Sampling without replacement; the hypergeometric distribution [65] --
4.6 Indefinite sampling; the geometric and negative binomial distributions [68] --
4.7 Sampling from a continuum: the Poisson process [71] --
4.8 'Nearest neighbours'; the exponential and gamma distributions [73] --
4.9 Other simple processes [74] --
5 Conditioning [80] --
5.1 Conditional expectation [80] --
5.2 Conditional probability [84] --
5.3 A conditional expectat ion as a random v aria ble [88] --
5.4 4 Conditioning on a a-field of events [90] --
5.5 Statistical independence [93] --
5.6 Elementary consequences of independence [95] --
5.7 Partial independence ; orthogonality [101] --
6 Applications of the Independence Concept [104] --
6.1 Mean square convergence of sample average [104] --
6.2 Convergence of sample average*. some slrongrr result [106] --
6.3 Renewal processes [109] --
6.4 Recurrent slates (events) [113] --
6.5 A result in statistical mechanics [117] --
6.6 Branching processes [120] --
7 Markov Processes [128] --
7.1 The Markov propery [121] --
7.2 Some particular Markov processes [133] --
7.3 The simple randmon walk [37] --
7.4 Markov processes in continuous time [139] --
7.5 The Poisson processes in time [141] --
7.6 Birth processes [144] --
7.7 Birth and death processes. [147] --
8 Continuous Distributions [150] --
8.1 Distributions whith a density [150] --
8.2 Functions of randmon variables [153] --
8.3 Conditional densities [159] --
8.4 Characteristic functions [161] --
8.5 The normal distribution; normal convergence [167] --
8.6 A direct proof of norma convergence [171] --
9 Convergence of Randmon Sequences 174 9.1 Characterizacion of convergence [174] --
9.2 Types of convergence [176] --
9.3 Some consequences [178] --
9.4 Kolmogorov´s inequality, and refenements of it [180] --
9.5 The laws of large numbers [183] --
9.6 Martingale convergence, and applications [186] --
9.7 Convergence in rth mean [189] --
10 Extension [194] --
10.1 Extension of the expectation functional :he finite case [194] --
10.2 Generalities on the infinite case [197] --
10.3 Extension on a linear lattice [199] --
10.4 Extension on a quadratic field [201] --
11 Examples of Extension [204] --
11.1 Integrable functions of a scalar random variable [204] --
11.2 Expectations derivable from the characteristic function [206] --
12 Some Interesting Processes [212] --
12.1 Quantum mechanics [212] --
12.2 Information theory [218] --
12.3 Dynamic programming; stock control [223] --
12.4 Stochastic differential equations: generalized processes [227] --
References [233] --
Index [235] --

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