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1.

図書
図書
1. Probability and statistics for computer scientists. 3rd ed (: hardback)
Michael Baron
出版情報: Boca Raton, FL : CRC Press, c2019  xix, 465 p. ; 27 cm
シリーズ名: A Chapman & Hall book
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目次情報: 続きを見る
Preface
Introduction and Overview / 1：
Making decisions under uncertainty / 1.1：
Overview of this book / 1.2：
Summary and conclusions
Exercises
Probability and Random Variables / I：
Probability / 2：
Events and their probabilities / 2.1：
Outcomes, events, and the sample space / 2.1.1：
Set operations / 2.1.2：
Rules of Probability / 2.2：
Axioms of Probability / 2.2.1：
Computing probabilities of events / 2.2.2：
Applications in reliability / 2.2.3：
Combinatorics / 2.3：
Equally likely outcomes / 2.3.1：
Permutations and combinations / 2.3.2：
Conditional probability and independence / 2.4：
Discrete Random Variables and Their Distributions / 3：
Distribution of a random variable / 3.1：
Main concepts / 3.1.1：
Types of random variables / 3.1.2：
Distribution of a random vector / 3.2：
Joint distribution and marginal distributions / 3.2.1：
Independence of random variables / 3.2.2：
Expectation and variance / 3.3：
Expectation / 3.3.1：
Expectation of a function / 3.3.2：
Properties / 3.3.3：
Variance and standard deviation / 3.3.4：
Covariance and correlation / 3.3.5：
Chebyshev's inequality / 3.3.6：
Application to finance / 3.3.8：
Families of discrete distributions / 3.4：
Bernoulli distribution / 3.4.1：
Binomial distribution / 3.4.2：
Geometric distribution / 3.4.3：
Negative Binomial distribution / 3.4.4：
Poisson distribution / 3.4.5：
Poisson approximation of Binomial distribution / 3.4.6：
Continuous Distributions / 4：
Probability density / 4.1：
Families of continuous distributions / 4.2：
Uniform distribution / 4.2.1：
Exponential distribution / 4.2.2：
Gamma distribution / 4.2.3：
Normal distribution / 4.2.4：
Central Limit Theorem / 4.3：
Computer Simulations and Monte Carlo Methods / 5：
Introduction / 5.1：
Applications and examples / 5.1.1：
Simulation of random variables / 5.2：
Random number generators / 5.2.1：
Discrete methods / 5.2.2：
Inverse transform method / 5.2.3：
Rejection method / 5.2.4：
Generation of random vectors / 5.2.5：
Special methods / 5.2.6：
Solving problems by Monte Carlo methods / 5.3：
Estimating probabilities / 5.3.1：
Estimating means and standard deviations / 5.3.2：
Forecasting / 5.3.3：
Estimating lengths, areas, and volumes / 5.3.4：
Monte Carlo integration / 5.3.5：
Stochastic Processes / II：
Definitions and classifications / 6：
Markov processes and Markov chains / 6.2：
Markov chains / 6.2.1：
Matrix approach / 6.2.2：
Steady-state distribution / 6.2.3：
Counting processes / 6.3：
Binomial process / 6.3.1：
Poisson process / 6.3.2：
Simulation of stochastic processes / 6.4：
Queuing Systems / 7：
Main components of a queuing system / 7.1：
The Little's Law / 7.2：
Bernoulli single-server queuing process / 7.3：
Systems with limited capacity / 7.3.1：
M/M/1 system / 7.4：
Evaluating the system's performance / 7.4.1：
Multiserver queuing systems / 7.5：
Bernoulli k-server queuing process / 7.5.1：
M/M/k systems / 7.5.2：
Unlimited number of servers and M/M/∞ / 7.5.3：
Simulation of queuing systems / 7.6：
Statistics / III：
Introduction to Statistics / 8：
Population and sample, parameters and statistics / 8.1：
Descriptive statistics / 8.2：
Mean / 8.2.1：
Median / 8.2.2：
Quantiles, percentiles, and quartiles / 8.2.3：
Standard errors of estimates / 8.2.4：
Interquartile range / 8.2.6：
Graphical statistics / 8.3：
Histogram / 8.3.1：
Stem-and-leaf plot / 8.3.2：
Boxplot / 8.3.3：
Scatter plots and time plots / 8.3.4：
Statistical Inference I / 9：
Parameter estimation / 9.1：
Method of moments / 9.1.1：
Method of maximum likelihood / 9.1.2：
Estimation of standard errors / 9.1.3：
Confidence intervals / 9.2：
Construction of confidence intervals: a general method / 9.2.1：
Confidence interval for the population mean / 9.2.2：
Confidence interval for the difference between two means / 9.2.3：
Selection of a sample size / 9.2.4：
Estimating means with a given precision / 9.2.5：
Unknown standard deviation / 9.3：
Large samples / 9.3.1：
Confidence intervals for proportions / 9.3.2：
Estimating proportions with a given precision / 9.3.3：
Small samples: Student's t distribution / 9.3.4：
Comparison of two populations with unknown variances / 9.3.5：
Hypothesis testing / 9.4：
Hypothesis and alternative / 9.4.1：
Type I and Type II errors: level of significance / 9.4.2：
Level ¿ tests: general approach / 9.4.3：
Rejection regions and power / 9.4.4：
Standard Normal null distribution (Z-test) / 9.4.5：
Z-tests for means and proportions / 9.4.6：
Pooled sample proportion / 9.4.7：
Unknown ¿: T-tests / 9.4.8：
Duality: two-sided tests and two-sided confidence intervals / 9.4.9：
P-value / 9.4.10：
Inference about variances / 9.5：
Variance estimator and Chi-square distribution / 9.5.1：
Confidence interval for the population variance / 9.5.2：
Testing variance / 9.5.3：
Comparison of two variances. F-distribution / 9.5.4：
Confidence interval for the ratio of population variances / 9.5.5：
F-tests comparing two variances / 9.5.6：
Statistical Inference II / 10：
Chi-square tests / 10.1：
Testing a distribution / 10.1.1：
Testing a family of distributions / 10.1.2：
Testing independence / 10.1.3：
Nonparametric statistics / 10.2：
Sign test / 10.2.1：
Wilcoxon signed rank test / 10.2.2：
Mann-Whitney-Wilcoxon rank sum test / 10.2.3：
Bootstrap / 10.3：
Bootstrap distribution and all bootstrap samples / 10.3.1：
Computer generated bootstrap samples / 10.3.2：
Bootstrap confidence intervals / 10.3.3：
Bayesian inference / 10.4：
Prior and posterior / 10.4.1：
Bayesian estimation / 10.4.2：
Bayesian credible sets / 10.4.3：
Bayesian hypothesis testing / 10.4.4：
Regression / 11：
Least squares estimation / 11.1：
Examples / 11.1.1：
Method of least squares / 11.1.2：
Linear regression / 11.1.3：
Regression, and correlation / 11.1.4：
Overfitting a model / 11.1.5：
Analysis of variance, prediction, and further inference / 11.2：
ANOVA and R-square / 11.2.1：
Tests and confidence intervals / 11.2.2：
Prediction / 11.2.3：
Multivariate regression / 11.3：
Introduction and examples / 11.3.1：
Matrix approach and least squares estimation / 11.3.2：
Analysis of variance, tests, and prediction / 11.3.3：
Model building / 11.4：
Adjusted R-square / 11.4.1：
Extra sum of squares, partial F-tests, and variable selection / 11.4.2：
Categorical predictors and dummy variables / 11.4.3：
Appendix
Data sets / A.1：
Inventory of distributions / A.2：
Discrete families / A.2.1：
Continuous families / A.2.2：
Distribution tables / A.3：
Calculus review / A.4：
Inverse function / A.4.1：
Limits and continuity / A.4.2：
Sequences and series / A.4.3：
Derivatives, minimum, and maximum / A.4.4：
Integrals / A.4.5：
Matrices and linear systems / A.5：
Answers to selected exercises / A.6：
Index
Preface
Introduction and Overview / 1：
Making decisions under uncertainty / 1.1：
2.

図書
図書
2. Introduction to probability (: hardback)
Joseph K. Blitzstein, Jessica Hwang
出版情報: Boca Raton, Fla. : CRC Press, c2015  xv, 580 p. ; 27 cm
シリーズ名: Texts in statistical science
A Chapman & Hall book
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3.

図書
図書
3. Probability : the science of uncertainty with applications to investments, insurance, and engineering
Michael A. Bean
出版情報: Providence, R.I. : American Mathematical Society, 2009, c2001  xiii, 448 p. ; 24 cm
シリーズ名: The Sally series ; . Pure and applied undergraduate texts ; 6
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目次情報: 続きを見る
Introduction
A survey of some basic concepts through examples
Classical probability
Random variables and probability distributions
Special discrete distributions
Special continuous distributions
Transformations of random variables
Sums and products of random variables
Mixtures and compound distributions
The Markowitz investment portfolio selection model
Appendixes
Answers to selected exercises
Index
Introduction
A survey of some basic concepts through examples
Classical probability
4.

図書
図書
4. Basic probability : what every math student should know. 2nd ed (:hbk)
Henk Tijms
出版情報: Singapore : World Scientific, c2021  viii, 175 p. ; 24 cm
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5.

図書
図書
5. A graduate course in probability (: hbk.)
Liviu I Nicolaescu
出版情報: Singapore : World Scientific, c2023  xvi, 541 p. ; 25 cm
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6.

図書
図書
6. Introduction to probability : multivariate models and applications (v. 2 : hardcover)
N. Balakrishnan, Markos V. Koutras, Konstantinos G. Politis
出版情報: Hoboken, N.J. : Wiley, 2022  xv, 528 p. ; 27 cm
シリーズ名: Wiley series in probability and mathematical statistics
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7.

電子ブック
ＥＢ
7. Probability : theory and examples. 5th ed (: electronic bk)
Rick Durrett
出版情報:   1 online resource (xii, 419 p.)
シリーズ名: Cambridge series in statistical and probabilistic mathematics ; 49
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8.

図書
図書
8. Introduction to probability and statistics. 15th ed., Student ed
William Mendenhall, III, Robert J. Beaver, Barbara M. Beaver
出版情報: Boston, Mass. : Cengage, c2020  xxi, 760 p. ; 27 cm
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9.

電子ブック
ＥＢ
9. Probability on graphs : random processes on graphs and lattices. Second edition (: electronic bk)
Geoffrey Grimmett, Statistical Laboratory, University of Cambridge
出版情報:   1 online resource (xi, 265 p.)
シリーズ名: Institute of Mathematical Statistics textbooks ; 8
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10.

電子ブック
ＥＢ
10. Thinking probabilistically : : stochastic processes, disordered systems, and their applications ((ebook))
Ariel Amir
出版情報:   1 online resource (vii, 233 pages)
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