Normal view

## Introductory probability and statistical applications / Paul L. Meyer.

Editor: Reading, Mass. : Addison-Wesley, c1970Edición: 2nd edDescripción: xiv, 367 p. : il. ; 25 cmISBN: 0201047101Otra clasificación: 60-01
Contenidos:
```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]
15.4 Goodness of fit tests [328]
References [338]
Appendix [341]
Index [363]```
Item type Home library Shelving location Call number Materials specified Status Date due Barcode Course reserves
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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] --
15.4 Goodness of fit tests [328] --
References [338] --
Appendix [341] --
Answers to Selected Problems [357] --
Index [363] --

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