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Probability with STEM Applications

Häftad, Engelska, 2021

1 673 kr

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Beskrivning

Probability with STEM Applications, Third Edition, is an accessible and well-balanced introduction to post-calculus applied probability. Integrating foundational mathematical theory and the application of probability in the real world, this leading textbook engages students with unique problem scenarios and more than 1100 exercises of varying levels of difficulty. The text uses a hands-on, software-oriented approach to the subject of probability. MATLAB and R examples and exercises — complemented by computer code that enables students to create their own simulations — demonstrate the importance of software to solve problems that cannot be obtained analytically.Revised and updated throughout, the textbook covers basic properties of probability, random variables and their probability distributions, a brief introduction to statistical inference, Markov chains, stochastic processes, and signal processing. This new edition is the perfect text for a one-semester course and contains enough additional material for an entire academic year. The blending of theory and application will appeal not only to mathematics and statistics majors but also to engineering students, and quantitative business and social science majors.New to this Edition: Offered as a traditional textbook and in enhanced ePub format, containing problems with show/hide solutions and interactive applets and illustrationsRevised and expanded chapters on conditional probability and independence, families of continuous distributions, and Markov chainsNew problems and updated problem sets throughoutFeatures: Introduces basic theoretical knowledge in the first seven chapters, serving as a self-contained textbook of roughly 650 problemsProvides numerous up-to-date examples and problems in R and MATLABDiscusses examples from recent journal articles, classic problems, and various practical applicationsIncludes a chapter specifically designed for electrical and computer engineers, suitable for a one-term class on random signals and noiseContains appendices of statistical tables, background mathematics, and important probability distributions

Produktinformation

Utgivningsdatum:2021-03-04
Mått:201 x 249 x 28 mm
Vikt:1 089 g
Format:Häftad
Språk:Engelska
Antal sidor:640
Upplaga:3
Förlag:John Wiley & Sons Inc
ISBN:9781119717867

Utforska kategorier

Matematisk statistik inom Naturvetenskap och teknik

Innehållsförteckning

Preface xvIntroduction 1Why Study Probability? 1Software Use in Probability 2Modern Application of Classic Probability Problems 2Applications to Business 3Applications to the Life Sciences 4Applications to Engineering and Operations Research 4Applications to Finance 6Probability in Everyday Life 71 Introduction to Probability 13Introduction 131.1 Sample Spaces and Events 13The Sample Space of an Experiment 13Events 15Some Relations from Set Theory 16Exercises Section 1.1 (1–12) 181.2 Axioms Interpretations and Properties of Probability 19Interpreting Probability 21More Probability Properties 23Contingency Tables 25Determining Probabilities Systematically 26Equally Likely Outcomes 27Exercises Section 1.2 (13–30) 281.3 Counting Methods 30The Fundamental Counting Principle 31Tree Diagrams 32Permutations 33Combinations 34Partitions 38Exercises Section 1.3 (31–50) 39Supplementary Exercises (51–62) 422 Conditional Probability and Independence 45Introduction 452.1 Conditional Probability 45The Definition of Conditional Probability 46The Multiplication Rule for P(A ∩ B) 492.2 The Law of Total Probability and Bayes’ Theorem 52The Law of Total Probability 52Bayes’ Theorem 55Exercises Section 2.2 (17–32) 592.3 Independence 61The Multiplication Rule for Independent Events 63Independence of More Than Two Events 65Exercises Section 2.3 (33–54) 662.4 Simulation of Random Events 69The Backbone of Simulation: Random Number Generators 70Precision of Simulation 73Exercises Section 2.4 (55–74) 74Supplementary Exercises (75–100) 773 Discrete Probability Distributions:general Properties 82Introduction 823.1 Random Variables 82Two Types of Random Variables 84Exercises Section 3.1 (1–10) 853.2 Probability Distributions for Discrete Random Variables 86Another View of Probability Mass Functions 89Exercises Section 3.2 (11–21) 903.3 The Cumulative Distribution Function 91Exercises Section 3.3 (22–30) 953.4 Expected Value and Standard Deviation 96The Expected Value of X 97The Expected Value of a Function 99The Variance and Standard Deviation of X 102Properties of Variance 104Exercises Section 3.4 (31–50) 1053.5 Moments and Moment Generating Functions 108The Moment Generating Function 109Obtaining Moments from the MGF 111Exercises Section 3.5 (51–64) 1133.6 Simulation of Discrete Random Variables 114Simulations Implemented in R and Matlab 117Simulation Mean Standard Deviation and Precision 117Exercises Section 3.6 (65–74) 119Supplementary Exercises (75–84) 1204 Families of Discrete Distributions 122Introduction 1224.1 Parameters and Families of Distributions 122Exercises Section 4.1 (1–6) 1244.2 The Binomial Distribution 125The Binomial Random Variable and Distribution 127Computing Binomial Probabilities 129The Mean Variance and Moment Generating Function 130Binomial Calculations with Software 132Exercises Section 4.2 (7–34) 1324.3 The Poisson Distribution 136The Poisson Distribution as a Limit 137The Mean Variance and Moment Generating Function 139The Poisson Process 140Poisson Calculations with Software 141Exercises Section 4.3 (35–54) 1424.4 The Hypergeometric Distribution 145Mean and Variance 148Hypergeometric Calculations with Software 149Exercises Section 4.4 (55–64) 1494.5 The Negative Binomial and Geometric Distributions 151The Geometric Distribution 152Mean Variance and Moment Generating Function 152Alternative Definitions of the Negative Binomial Distribution 153Negative Binomial Calculations with Software 154Exercises Section 4.5 (65–78) 154Supplementary Exercises (79–100) 1565 Continuous Probability Distributions:general Properties 160Introduction 1605.1 Continuous Random Variables and Probability Density Functions 160Probability Distributions for Continuous Variables 161Exercises Section 5.1 (1–8) 1655.2 The Cumulative Distribution Function and Percentiles 166Using F(x) to Compute Probabilities 168Obtaining f(x) fromF(x) 169Percentiles of a Continuous Distribution 169Exercises Section 5.2 (9–18) 1715.3 Expected Values Variance and Moment Generating Functions 173Expected Values 173Variance and Standard Deviation 175Properties of Expectation and Variance 176Moment Generating Functions 177Exercises Section 5.3 (19–38) 1795.4 Transformation of a Random Variable 181Exercises Section 5.4 (39–54) 1855.5 Simulation of Continuous Random Variables 186The Inverse CDF Method 186The Accept–Reject Method 189Precision of Simulation Results 191Exercises Section 5.5 (55–63) 191Supplementary Exercises (64–76) 1936 Families of Continuous Distributions 196Introduction 1966.1 The Normal (Gaussian) Distribution 196The Standard Normal Distribution 197Arbitrary Normal Distributions 199The Moment Generating Function 203Normal Distribution Calculations with Software 204Exercises Section 6.1 (1–27) 2056.2 Normal Approximation of Discrete Distributions 208Approximating the Binomial Distribution 209Exercises Section 6.2 (28–36) 2116.3 The Exponential and Gamma Distributions 212The Exponential Distribution 212The Gamma Distribution 214The Gamma and Exponential MGFs 217Gamma and Exponential Calculations with Software 218Exercises Section 6.3 (37–50) 2186.4 Other Continuous Distributions 220The Weibull Distribution 220The Lognormal Distribution 222The Beta Distribution 224Exercises Section 6.4 (51–66) 2266.5 Probability Plots 228Sample Percentiles 228A Probability Plot 229Departures from Normality 232Beyond Normality 234Probability Plots in Matlab and R 236Exercises Section 6.5 (67–76) 237Supplementary Exercises (77–96) 2387 Joint Probability Distributions 242Introduction 2427.1 Joint Distributions for Discrete Random Variables 242The Joint Probability Mass Function for Two Discrete Random Variables 242Marginal Probability Mass Functions 244Independent Random Variables 245More Than Two Random Variables 246Exercises Section 7.1 (1–12) 2487.2 Joint Distributions for Continuous Random Variables 250The Joint Probability Density Function for Two Continuous Random Variables 250Marginal Probability Density Functions 252Independence of Continuous Random Variables 254More Than Two Random Variables 255Exercises Section 7.2 (13–22) 2577.3 Expected Values Covariance and Correlation 258Properties of Expected Value 260Covariance 261Correlation 263Correlation Versus Causation 265Exercises Section 7.3 (23–42) 2667.4 Properties of Linear Combinations 267Expected Value and Variance of a Linear Combination 268The PDF of a Sum 271Moment Generating Functions of Linear Combinations 273Exercises Section 7.4 (43–65) 2757.5 The Central Limit Theorem and the Law of Large Numbers 278Random Samples 278The Central Limit Theorem 282A More General Central Limit Theorem 286Other Applications of the Central Limit Theorem 287The Law of Large Numbers 288Proof of the Central Limit Theorem 290Exercises Section 7.5 (66–82) 2907.6 Simulation of Joint Probability Distributions 293Simulating Values from a Joint PMF 293Simulating Values from a Joint PDF 295Exercises Section 7.6 (83–90) 297Supplementary Exercises (91–124) 2988 Joint Probability Distributions:additional Topics 304Introduction 3048.1 Conditional Distributions and Expectation 304Conditional Distributions and Independence 306Conditional Expectation and Variance 307The Laws of Total Expectation and Variance 308Exercises Section 8.1 (1–18) 3138.2 The Bivariate Normal Distribution 315Conditional Distributions of X and Y 317Regression to the Mean 318The Multivariate Normal Distribution 319Bivariate Normal Calculations with Software 319Exercises Section 8.2 (19–30) 3208.3 Transformations of Jointly Distributed Random Variables 321The Joint Distribution of Two New Random Variables 322The Distribution of a Single New RV 323The Joint Distribution of More Than Two New Variables 325Exercises Section 8.3 (31–38) 3268.4 Reliability 327The Reliability Function 327Series and Parallel System Designs 329Mean Time to Failure 331The Hazard Function 332Exercises Section 8.4 (39–50) 3358.5 Order Statistics 337The Distributions of Yn and Y1 337The Distribution of the ith Order Statistic 339The Joint Distribution of All n Order Statistics 340Exercises Section 8.5 (51–60) 3428.6 Further Simulation Tools for Jointly Distributed Random Variables 343The Conditional Distribution Method of Simulation 343Simulating a Bivariate Normal Distribution 344Simulation Methods for Reliability 346Exercises Section 8.6 (61–68) 347Supplementary Exercises (69–82) 3489 the Basics of Statistical Inference 351Introduction 3519.1 Point Estimation 351Estimates and Estimators 352Assessing Estimators: Accuracy and Precision 354Exercises Section 9.1 (1–18) 3579.2 Maximum Likelihood Estimation 360Some Properties of MLEs 366Exercises Section 9.2 (19–30) 3679.3 Statistical Intervals 368Constructing a Confidence Interval 369Confidence Intervals for a Population Proportion 369Confidence Intervals for a Population Mean 371Further Comments on Statistical Intervals 375Confidence Intervals with Software 375Exercises Section 9.3 (31–48) 3769.4 Hypothesis Tests 379Hypotheses and Test Procedures 380Hypothesis Testing for a Population Mean 381Errors in Hypothesis Testing and the Power of a Test 385Hypothesis Testing for a Population Proportion 388Software for Hypothesis Test Calculations 389Exercises Section 9.4 (49–71) 3919.5 Bayesian Estimation 393The Posterior Distribution of a Parameter 394Inferences from the Posterior Distribution 397Further Comments on Bayesian Inference 398Exercises Section 9.5 (72–80) 3999.6 Simulation-Based Inference 400The Bootstrap Method 400Interval Estimation Using the Bootstrap 402Hypothesis Tests Using the Bootstrap 404More on Simulation-Based Inference 405Exercises Section 9.6 (81–90) 405Supplementary Exercises (91–116) 40710 Markov Chains 411Introduction 41110.1 Terminology and Basic Properties 411The Markov Property 413Exercises Section 10.1 (1–10) 41610.2 The Transition Matrix and the Chapman–Kolmogorov Equations 418The Transition Matrix 418Computation of Multistep Transition Probabilities 419Exercises Section 10.2 (11–22) 42310.3 Specifying an Initial Distribution 426A Fixed Initial State 428Exercises Section 10.3 (23–30) 42910.4 Regular Markov Chains and the Steady-State Theorem 430Regular Chains 431The Steady-State Theorem 432Interpreting the Steady-State Distribution 433Efficient Computation of Steady-State Probabilities 435Irreducible and Periodic Chains 437Exercises Section 10.4 (31–43) 43810.5 Markov Chains with Absorbing States 440Time to Absorption 441Mean Time to Absorption 444Mean First Passage Times 448Probabilities of Eventual Absorption 449Exercises Section 10.5 (44–58) 45110.6 Simulation of Markov Chains 453Exercises Section 10.6 (59–66) 459Supplementary Exercises (67–82) 46111 Random Processes 465Introduction 46511.1 Types of Random Processes 465Classification of Processes 468Random Processes and Their Associated Random Variables 469Exercises Section 11.1 (1–10) 47011.2 Properties of the Ensemble: Mean and Autocorrelation Functions 471Mean and Variance Functions 471Autocovariance and Autocorrelation Functions 475The Joint Distribution of Two Random Processes 477Exercises Section 11.2 (11–24) 47811.3 Stationary and Wide-Sense Stationary Processes 479Properties of WSS Processes 483Ergodic Processes 486Exercises Section 11.3 (25–40) 48811.4 Discrete-Time Random Processes 489Special Discrete Sequences 491Exercises Section 11.4 (41–52) 493Supplementary Exercises (53–64) 49412 Families of Random Processes 497Introduction 49712.1 Poisson Processes 497Relation to Exponential and Gamma Distributions 499Combining and Decomposing Poisson Processes 502Alternative Definition of a Poisson Process 504Nonhomogeneous Poisson Processes 505The Poisson Telegraphic Process 506Exercises Section 12.1 (1–18) 50712.2 Gaussian Processes 509Brownian Motion 510Brownian Motion as a Limit 512Further Properties of Brownian Motion 512Variations on Brownian Motion 514Exercises Section 12.2 (19–28) 51512.3 Continuous-Time Markov Chains 516Infinitesimal Parameters and Instantaneous Transition Rates 518Sojourn Times and Transitions 520Long-Run Behavior of Continuous-Time Markov Chains 523Explicit Form of the Transition Matrix 526Exercises Section 12.3 (29–40) 527Supplementary Exercises (41–51) 52913 Introduction to Signal Processing 532Introduction 53213.1 Power Spectral Density 532Expected Power and the Power Spectral Density 532Properties of the Power Spectral Density 535Power in a Frequency Band 538White Noise Processes 539Cross-Power Spectral Density for Two Processes 541Exercises Section 13.1 (1–21) 54213.2 Random Processes and LTI Systems 544Properties of the LTI System Output 545Ideal Filters 548Signal Plus Noise 551Exercises Section 13.2 (22–38) 55413.3 Discrete-Time Signal Processing 556Random Sequences and LTI Systems 558Sampling Random Sequences 560Exercises Section 13.3 (39–50) 562A Statistical Tables A- 1A. 1 Binomial CDF A- 1A. 2 Poisson CDF A- 4A. 3 Standard Normal CDF A- 5A. 4 Incomplete Gamma Function A- 7A. 5 Critical Values for t Distributions A- 7A. 6 Tail Areas of t Distributions A- 9B Background Mathematics A- 13B. 1 Trigonometric Identities A- 13B. 2 Special Engineering Functions A- 13B. 3 o(h) Notation A- 14B. 4 The Delta Function A- 14B. 5 Fourier Transforms A- 15B. 6 Discrete-Time Fourier Transforms A- 16C Important Probability Distributions A- 18C. 1 Discrete Distributions A- 18C. 2 Continuous Distributions A- 20C. 3 Matlab and R Commands A- 23Bibliography B- 1Answers to Odd-numbered Exercises S- 1Index I- 1