Introductory probability and statistical applications / Paul L. Meyer.
Series Addison-Wesley series in statisticsEditor: Reading, Mass. : Addison-Wesley, c1970Edición: 2nd edDescripción: xiv, 367 p. : il. ; 25 cmISBN: 0201047101Otra clasificación: 60-01Chapter 1 Introduction to Probability 1.1 Mathematical models [1] 1.2 Introduction to sets [3] 1.3 Examples of nondeterministic experiments [6] 1.4 The sample space [8] 1.5 Events [10] 1.6 Relative frequency [12] 1.7 Basic notions of probability [13] 1.8 Several remarks [17] Chapter 2 Finite Sample Spaces 2.1 Finite sample spaces [21] 2.2 Equally likely outcomes [22] 2.3 Methods of enumeration [24] Chapter 3 Conditional Probability and Independence 3.1 Conditional probability [33] 3.2 Bayes’ theorem [39] 3.3 Independent events [41] 3.4 Schematic considerations; conditional probability and independence [46] Chapter 4 One-Dimensional Random Variables 4.1 General notion of a random variable [54] 4.2 Discrete random variables [59] 4.3 The binomial distribution [62] 4.4 Continuous random variables [66] 4.5 Cumulative distribution function [70] 4.6 Mixed distributions [73] 4.7 Uniformly distributed random variables [74] 4.8 A remark [76] Chapter 5 Functions of Random Variables 5.1 An example [81] 5.2 Equivalent events [81] 5.3 Discrete random variables [84] 5.4 Continuous random variables [85] Chapter 6 Two- and Higher-Dimensional Random Variables 6.1 Two-dimensional random variables [93] 6.2 Marginal and conditional probability distributions [99] 6.3 Independent random variables [103] 6.4 Functions of a random variable [106] 6.5 Distribution of product and quotient of independent random variables [109] 6.6 n-dimensional random variables [112] Chapter 7 Further Characterization of Random Variables 7.1 The expected value of a random variable [117] 7.2 Expectation of a function of a random variable [123] 7.3 Two-dimensional random variables [127] 7.4 Properties of expected value [128] 7.5 The variance of a random variable [134] 7.6 Properties of the variance of a random variable [136] 7.7 Approximate expressions for expectation and variance [139] 7.8 Chebyshev’s inequality [141] 7.9 The correlation coefficient [144] 7.10 Conditional expectation [148] 7.11 Regression of the mean [150] Chapter 8 The Poisson and Other Discrete Random Variables 8.1 The Poisson distribution [159] 8.2 The Poisson distribution as an approximation to the binomial distribution [160] 8.3 The Poisson process [165] 8.4 The geometric distribution [170] 8.5 The Pascal distribution [173] 8.6 Relationship between the binomial and Pascal distributions [174] 8.7 The hypergeometric distribution [175] 8.8 The multinomial distribution [176] Chapter 9 Some Important Continuous Random Variables 9.1 Introduction [182] 9.2 The normal distribution [182] 9.3 Properties of the normal distribution [183] 9.4 Tabulation of the normal distribution [.186] 9.5 The exponential distribution [190] 9.6 Properties of the exponential distribution [190] 9.7 The Gamma distribution [193] 9.8 Properties of the Gamma distribution [194] 9.9 The chi-square distribution [196] 9.10 Comparisons among various distributions [198] 9.11 The bivariate normal distribution [199] 9.12 Truncated distributions [200] Chapter 10 The Moment-Generating Function 10.1 Introduction [209] 10.2 The moment-generating function [210] 10.3 Examples of moment-generating functions [211] 10.4 Properties of the moment-generating function [213] 10.5 Reproductive properties [217] 10.6 Sequences of random variables [221] 10.7 Final remark [222] Chapter 11 Applications to Reliability Theory 11.1 Basic concepts [225] 11.2 The normal failure law [228] 11.3 The exponential failure law [229] 11.4 The exponential failure law and the Poisson distribution [232] 11.5 The Weibull failure law [234] 11.6 Reliability of systems [235] Chapter 12 Sums of Random Variables 12.1 Introduction [244] 12.2 The law of large numbers [244] 12.3 Normal approximation to the Binomial distribution [247] 12.4 The central limit theorem [250] 12.5 Other distributions approximated by the normal distribution: Poisson, Pascal, and Gamma [255] 12.6 The distribution of the sum of a finite number of random variables [256] Chapter 13 Samples and Sampling Distributions 13.1 Introduction [265] 13.2 Random samples [266] 13.3 Statistics [268] 13.4 Some important statistics [269] 13.5 The integral transform [275] Chapter 14 Estimation of Parameters 14.1 Introduction [282] 14.2 Criteria for estimates [283] 14.3 Some examples [286] 14.4 Maximum likelihood estimates [290] 14.5 The method of least squares [299] 14.6 The correlation coefficient [302] 14.7 Confidence intervals [303] 14.8 Student’s t-distribution [305] 14.9 More on confidence intervals [307] Chapter 15 Testing hypotheses 15.1 Introduction [316] 15.2 General formulation: normal distribution with known variance [321] 15.3 Additional examples [325] 15.4 Goodness of fit tests [328] References [338] Appendix [341] Answers to Selected Problems [357] Index [363]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 60 M6125-2 (Browse shelf) | Available | A-4165 |
Bibliografía: p. 338-339.
Chapter 1 Introduction to Probability --
1.1 Mathematical models [1] --
1.2 Introduction to sets [3] --
1.3 Examples of nondeterministic experiments [6] --
1.4 The sample space [8] --
1.5 Events [10] --
1.6 Relative frequency [12] --
1.7 Basic notions of probability [13] --
1.8 Several remarks [17] --
Chapter 2 Finite Sample Spaces --
2.1 Finite sample spaces [21] --
2.2 Equally likely outcomes [22] --
2.3 Methods of enumeration [24] --
Chapter 3 Conditional Probability and Independence --
3.1 Conditional probability [33] --
3.2 Bayes’ theorem [39] --
3.3 Independent events [41] --
3.4 Schematic considerations; conditional probability and independence [46] --
Chapter 4 One-Dimensional Random Variables --
4.1 General notion of a random variable [54] --
4.2 Discrete random variables [59] --
4.3 The binomial distribution [62] --
4.4 Continuous random variables [66] --
4.5 Cumulative distribution function [70] --
4.6 Mixed distributions [73] --
4.7 Uniformly distributed random variables [74] --
4.8 A remark [76] --
Chapter 5 Functions of Random Variables --
5.1 An example [81] --
5.2 Equivalent events [81] --
5.3 Discrete random variables [84] --
5.4 Continuous random variables [85] --
Chapter 6 Two- and Higher-Dimensional Random Variables --
6.1 Two-dimensional random variables [93] --
6.2 Marginal and conditional probability distributions [99] --
6.3 Independent random variables [103] --
6.4 Functions of a random variable [106] --
6.5 Distribution of product and quotient of independent random variables [109] --
6.6 n-dimensional random variables [112] --
Chapter 7 Further Characterization of Random Variables --
7.1 The expected value of a random variable [117] --
7.2 Expectation of a function of a random variable [123] --
7.3 Two-dimensional random variables [127] --
7.4 Properties of expected value [128] --
7.5 The variance of a random variable [134] --
7.6 Properties of the variance of a random variable [136] --
7.7 Approximate expressions for expectation and variance [139] --
7.8 Chebyshev’s inequality [141] --
7.9 The correlation coefficient [144] --
7.10 Conditional expectation [148] --
7.11 Regression of the mean [150] --
Chapter 8 The Poisson and Other Discrete Random Variables --
8.1 The Poisson distribution [159] --
8.2 The Poisson distribution as an approximation to the --
binomial distribution [160] --
8.3 The Poisson process [165] --
8.4 The geometric distribution [170] --
8.5 The Pascal distribution [173] --
8.6 Relationship between the binomial and Pascal distributions [174] --
8.7 The hypergeometric distribution [175] --
8.8 The multinomial distribution [176] --
Chapter 9 Some Important Continuous Random Variables --
9.1 Introduction [182] --
9.2 The normal distribution [182] --
9.3 Properties of the normal distribution [183] --
9.4 Tabulation of the normal distribution [.186] --
9.5 The exponential distribution [190] --
9.6 Properties of the exponential distribution [190] --
9.7 The Gamma distribution [193] --
9.8 Properties of the Gamma distribution [194] --
9.9 The chi-square distribution [196] --
9.10 Comparisons among various distributions [198] --
9.11 The bivariate normal distribution [199] --
9.12 Truncated distributions [200] --
Chapter 10 The Moment-Generating Function --
10.1 Introduction [209] --
10.2 The moment-generating function [210] --
10.3 Examples of moment-generating functions [211] --
10.4 Properties of the moment-generating function [213] --
10.5 Reproductive properties [217] --
10.6 Sequences of random variables [221] --
10.7 Final remark [222] --
Chapter 11 Applications to Reliability Theory --
11.1 Basic concepts [225] --
11.2 The normal failure law [228] --
11.3 The exponential failure law [229] --
11.4 The exponential failure law and the Poisson distribution [232] --
11.5 The Weibull failure law [234] --
11.6 Reliability of systems [235] --
Chapter 12 Sums of Random Variables --
12.1 Introduction [244] --
12.2 The law of large numbers [244] --
12.3 Normal approximation to the Binomial distribution [247] --
12.4 The central limit theorem [250] --
12.5 Other distributions approximated by the normal distribution: --
Poisson, Pascal, and Gamma [255] --
12.6 The distribution of the sum of a finite number of random variables [256] --
Chapter 13 Samples and Sampling Distributions --
13.1 Introduction [265] --
13.2 Random samples [266] --
13.3 Statistics [268] --
13.4 Some important statistics [269] --
13.5 The integral transform [275] --
Chapter 14 Estimation of Parameters --
14.1 Introduction [282] --
14.2 Criteria for estimates [283] --
14.3 Some examples [286] --
14.4 Maximum likelihood estimates [290] --
14.5 The method of least squares [299] --
14.6 The correlation coefficient [302] --
14.7 Confidence intervals [303] --
14.8 Student’s t-distribution [305] --
14.9 More on confidence intervals [307] --
Chapter 15 Testing hypotheses --
15.1 Introduction [316] --
15.2 General formulation: normal distribution with known variance [321] --
15.3 Additional examples [325] --
15.4 Goodness of fit tests [328] --
References [338] --
Appendix [341] --
Answers to Selected Problems [357] --
Index [363] --
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