{"product_id":"probability-with-stem-applications-isbn-9781119717867","title":"Probability with STEM Applications","description":"\u003cp\u003e\u003ci\u003eProbability with STEM Applications, Third Edition\u003c\/i\u003e, 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.\u003c\/p\u003e \u003cp\u003eRevised 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.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eNew to this Edition:\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eOffered as a traditional textbook and in enhanced ePub format, containing problems with show\/hide solutions and interactive applets and illustrations\u003c\/li\u003e \u003cli\u003eRevised and expanded chapters on conditional probability and independence, families of continuous distributions, and Markov chains\u003c\/li\u003e \u003cli\u003eNew problems and updated problem sets throughout\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003cb\u003eFeatures:\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eIntroduces basic theoretical knowledge in the first seven chapters, serving as a self-contained textbook of roughly 650 problems\u003c\/li\u003e \u003cli\u003eProvides numerous up-to-date examples and problems in R and MATLAB\u003c\/li\u003e \u003cli\u003eDiscusses examples from recent journal articles, classic problems, and various practical applications\u003c\/li\u003e \u003cli\u003eIncludes a chapter specifically designed for electrical and computer engineers, suitable for a one-term class on random signals and noise\u003c\/li\u003e \u003cli\u003eContains appendices of statistical tables, background mathematics, and important probability distributions\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003eWhy Study Probability? 1\u003c\/p\u003e \u003cp\u003eSoftware Use in Probability 2\u003c\/p\u003e \u003cp\u003eModern Application of Classic Probability Problems 2\u003c\/p\u003e \u003cp\u003eApplications to Business 3\u003c\/p\u003e \u003cp\u003eApplications to the Life Sciences 4\u003c\/p\u003e \u003cp\u003eApplications to Engineering and Operations Research 4\u003c\/p\u003e \u003cp\u003eApplications to Finance 6\u003c\/p\u003e \u003cp\u003eProbability in Everyday Life 7\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Probability 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Sample Spaces and Events 13\u003c\/p\u003e \u003cp\u003eThe Sample Space of an Experiment 13\u003c\/p\u003e \u003cp\u003eEvents 15\u003c\/p\u003e \u003cp\u003eSome Relations from Set Theory 16\u003c\/p\u003e \u003cp\u003eExercises Section 1.1 (1–12) 18\u003c\/p\u003e \u003cp\u003e1.2 Axioms Interpretations and Properties of Probability 19\u003c\/p\u003e \u003cp\u003eInterpreting Probability 21\u003c\/p\u003e \u003cp\u003eMore Probability Properties 23\u003c\/p\u003e \u003cp\u003eContingency Tables 25\u003c\/p\u003e \u003cp\u003eDetermining Probabilities Systematically 26\u003c\/p\u003e \u003cp\u003eEqually Likely Outcomes 27\u003c\/p\u003e \u003cp\u003eExercises Section 1.2 (13–30) 28\u003c\/p\u003e \u003cp\u003e1.3 Counting Methods 30\u003c\/p\u003e \u003cp\u003eThe Fundamental Counting Principle 31\u003c\/p\u003e \u003cp\u003eTree Diagrams 32\u003c\/p\u003e \u003cp\u003ePermutations 33\u003c\/p\u003e \u003cp\u003eCombinations 34\u003c\/p\u003e \u003cp\u003ePartitions 38\u003c\/p\u003e \u003cp\u003eExercises Section 1.3 (31–50) 39\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (51–62) 42\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Conditional Probability and Independence 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Conditional Probability 45\u003c\/p\u003e \u003cp\u003eThe Definition of Conditional Probability 46\u003c\/p\u003e \u003cp\u003eThe Multiplication Rule for P(A ∩ B) 49\u003c\/p\u003e \u003cp\u003e2.2 The Law of Total Probability and Bayes’ Theorem 52\u003c\/p\u003e \u003cp\u003eThe Law of Total Probability 52\u003c\/p\u003e \u003cp\u003eBayes’ Theorem 55\u003c\/p\u003e \u003cp\u003eExercises Section 2.2 (17–32) 59\u003c\/p\u003e \u003cp\u003e2.3 Independence 61\u003c\/p\u003e \u003cp\u003eThe Multiplication Rule for Independent Events 63\u003c\/p\u003e \u003cp\u003eIndependence of More Than Two Events 65\u003c\/p\u003e \u003cp\u003eExercises Section 2.3 (33–54) 66\u003c\/p\u003e \u003cp\u003e2.4 Simulation of Random Events 69\u003c\/p\u003e \u003cp\u003eThe Backbone of Simulation: Random Number Generators 70\u003c\/p\u003e \u003cp\u003ePrecision of Simulation 73\u003c\/p\u003e \u003cp\u003eExercises Section 2.4 (55–74) 74\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (75–100) 77\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Discrete Probability Distributions:general Properties 82\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 82\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Random Variables 82\u003c\/p\u003e \u003cp\u003eTwo Types of Random Variables 84\u003c\/p\u003e \u003cp\u003eExercises Section 3.1 (1–10) 85\u003c\/p\u003e \u003cp\u003e3.2 Probability Distributions for Discrete Random Variables 86\u003c\/p\u003e \u003cp\u003eAnother View of Probability Mass Functions 89\u003c\/p\u003e \u003cp\u003eExercises Section 3.2 (11–21) 90\u003c\/p\u003e \u003cp\u003e3.3 The Cumulative Distribution Function 91\u003c\/p\u003e \u003cp\u003eExercises Section 3.3 (22–30) 95\u003c\/p\u003e \u003cp\u003e3.4 Expected Value and Standard Deviation 96\u003c\/p\u003e \u003cp\u003eThe Expected Value of X 97\u003c\/p\u003e \u003cp\u003eThe Expected Value of a Function 99\u003c\/p\u003e \u003cp\u003eThe Variance and Standard Deviation of X 102\u003c\/p\u003e \u003cp\u003eProperties of Variance 104\u003c\/p\u003e \u003cp\u003eExercises Section 3.4 (31–50) 105\u003c\/p\u003e \u003cp\u003e3.5 Moments and Moment Generating Functions 108\u003c\/p\u003e \u003cp\u003eThe Moment Generating Function 109\u003c\/p\u003e \u003cp\u003eObtaining Moments from the MGF 111\u003c\/p\u003e \u003cp\u003eExercises Section 3.5 (51–64) 113\u003c\/p\u003e \u003cp\u003e3.6 Simulation of Discrete Random Variables 114\u003c\/p\u003e \u003cp\u003eSimulations Implemented in R and Matlab 117\u003c\/p\u003e \u003cp\u003eSimulation Mean Standard Deviation and Precision 117\u003c\/p\u003e \u003cp\u003eExercises Section 3.6 (65–74) 119\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (75–84) 120\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Families of Discrete Distributions 122\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 122\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Parameters and Families of Distributions 122\u003c\/p\u003e \u003cp\u003eExercises Section 4.1 (1–6) 124\u003c\/p\u003e \u003cp\u003e4.2 The Binomial Distribution 125\u003c\/p\u003e \u003cp\u003eThe Binomial Random Variable and Distribution 127\u003c\/p\u003e \u003cp\u003eComputing Binomial Probabilities 129\u003c\/p\u003e \u003cp\u003eThe Mean Variance and Moment Generating Function 130\u003c\/p\u003e \u003cp\u003eBinomial Calculations with Software 132\u003c\/p\u003e \u003cp\u003eExercises Section 4.2 (7–34) 132\u003c\/p\u003e \u003cp\u003e4.3 The Poisson Distribution 136\u003c\/p\u003e \u003cp\u003eThe Poisson Distribution as a Limit 137\u003c\/p\u003e \u003cp\u003eThe Mean Variance and Moment Generating Function 139\u003c\/p\u003e \u003cp\u003eThe Poisson Process 140\u003c\/p\u003e \u003cp\u003ePoisson Calculations with Software 141\u003c\/p\u003e \u003cp\u003eExercises Section 4.3 (35–54) 142\u003c\/p\u003e \u003cp\u003e4.4 The Hypergeometric Distribution 145\u003c\/p\u003e \u003cp\u003eMean and Variance 148\u003c\/p\u003e \u003cp\u003eHypergeometric Calculations with Software 149\u003c\/p\u003e \u003cp\u003eExercises Section 4.4 (55–64) 149\u003c\/p\u003e \u003cp\u003e4.5 The Negative Binomial and Geometric Distributions 151\u003c\/p\u003e \u003cp\u003eThe Geometric Distribution 152\u003c\/p\u003e \u003cp\u003eMean Variance and Moment Generating Function 152\u003c\/p\u003e \u003cp\u003eAlternative Definitions of the Negative Binomial Distribution 153\u003c\/p\u003e \u003cp\u003eNegative Binomial Calculations with Software 154\u003c\/p\u003e \u003cp\u003eExercises Section 4.5 (65–78) 154\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (79–100) 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Continuous Probability Distributions:general Properties 160\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 160\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Continuous Random Variables and Probability Density Functions 160\u003c\/p\u003e \u003cp\u003eProbability Distributions for Continuous Variables 161\u003c\/p\u003e \u003cp\u003eExercises Section 5.1 (1–8) 165\u003c\/p\u003e \u003cp\u003e5.2 The Cumulative Distribution Function and Percentiles 166\u003c\/p\u003e \u003cp\u003eUsing F(x) to Compute Probabilities 168\u003c\/p\u003e \u003cp\u003eObtaining f(x) fromF(x) 169\u003c\/p\u003e \u003cp\u003ePercentiles of a Continuous Distribution 169\u003c\/p\u003e \u003cp\u003eExercises Section 5.2 (9–18) 171\u003c\/p\u003e \u003cp\u003e5.3 Expected Values Variance and Moment Generating Functions 173\u003c\/p\u003e \u003cp\u003eExpected Values 173\u003c\/p\u003e \u003cp\u003eVariance and Standard Deviation 175\u003c\/p\u003e \u003cp\u003eProperties of Expectation and Variance 176\u003c\/p\u003e \u003cp\u003eMoment Generating Functions 177\u003c\/p\u003e \u003cp\u003eExercises Section 5.3 (19–38) 179\u003c\/p\u003e \u003cp\u003e5.4 Transformation of a Random Variable 181\u003c\/p\u003e \u003cp\u003eExercises Section 5.4 (39–54) 185\u003c\/p\u003e \u003cp\u003e5.5 Simulation of Continuous Random Variables 186\u003c\/p\u003e \u003cp\u003eThe Inverse CDF Method 186\u003c\/p\u003e \u003cp\u003eThe Accept–Reject Method 189\u003c\/p\u003e \u003cp\u003ePrecision of Simulation Results 191\u003c\/p\u003e \u003cp\u003eExercises Section 5.5 (55–63) 191\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (64–76) 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Families of Continuous Distributions 196\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 196\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 The Normal (Gaussian) Distribution 196\u003c\/p\u003e \u003cp\u003eThe Standard Normal Distribution 197\u003c\/p\u003e \u003cp\u003eArbitrary Normal Distributions 199\u003c\/p\u003e \u003cp\u003eThe Moment Generating Function 203\u003c\/p\u003e \u003cp\u003eNormal Distribution Calculations with Software 204\u003c\/p\u003e \u003cp\u003eExercises Section 6.1 (1–27) 205\u003c\/p\u003e \u003cp\u003e6.2 Normal Approximation of Discrete Distributions 208\u003c\/p\u003e \u003cp\u003eApproximating the Binomial Distribution 209\u003c\/p\u003e \u003cp\u003eExercises Section 6.2 (28–36) 211\u003c\/p\u003e \u003cp\u003e6.3 The Exponential and Gamma Distributions 212\u003c\/p\u003e \u003cp\u003eThe Exponential Distribution 212\u003c\/p\u003e \u003cp\u003eThe Gamma Distribution 214\u003c\/p\u003e \u003cp\u003eThe Gamma and Exponential MGFs 217\u003c\/p\u003e \u003cp\u003eGamma and Exponential Calculations with Software 218\u003c\/p\u003e \u003cp\u003eExercises Section 6.3 (37–50) 218\u003c\/p\u003e \u003cp\u003e6.4 Other Continuous Distributions 220\u003c\/p\u003e \u003cp\u003eThe Weibull Distribution 220\u003c\/p\u003e \u003cp\u003eThe Lognormal Distribution 222\u003c\/p\u003e \u003cp\u003eThe Beta Distribution 224\u003c\/p\u003e \u003cp\u003eExercises Section 6.4 (51–66) 226\u003c\/p\u003e \u003cp\u003e6.5 Probability Plots 228\u003c\/p\u003e \u003cp\u003eSample Percentiles 228\u003c\/p\u003e \u003cp\u003eA Probability Plot 229\u003c\/p\u003e \u003cp\u003eDepartures from Normality 232\u003c\/p\u003e \u003cp\u003eBeyond Normality 234\u003c\/p\u003e \u003cp\u003eProbability Plots in Matlab and R 236\u003c\/p\u003e \u003cp\u003eExercises Section 6.5 (67–76) 237\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (77–96) 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Joint Probability Distributions 242\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 242\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Joint Distributions for Discrete Random Variables 242\u003c\/p\u003e \u003cp\u003eThe Joint Probability Mass Function for Two Discrete Random Variables 242\u003c\/p\u003e \u003cp\u003eMarginal Probability Mass Functions 244\u003c\/p\u003e \u003cp\u003eIndependent Random Variables 245\u003c\/p\u003e \u003cp\u003eMore Than Two Random Variables 246\u003c\/p\u003e \u003cp\u003eExercises Section 7.1 (1–12) 248\u003c\/p\u003e \u003cp\u003e7.2 Joint Distributions for Continuous Random Variables 250\u003c\/p\u003e \u003cp\u003eThe Joint Probability Density Function for Two Continuous Random Variables 250\u003c\/p\u003e \u003cp\u003eMarginal Probability Density Functions 252\u003c\/p\u003e \u003cp\u003eIndependence of Continuous Random Variables 254\u003c\/p\u003e \u003cp\u003eMore Than Two Random Variables 255\u003c\/p\u003e \u003cp\u003eExercises Section 7.2 (13–22) 257\u003c\/p\u003e \u003cp\u003e7.3 Expected Values Covariance and Correlation 258\u003c\/p\u003e \u003cp\u003eProperties of Expected Value 260\u003c\/p\u003e \u003cp\u003eCovariance 261\u003c\/p\u003e \u003cp\u003eCorrelation 263\u003c\/p\u003e \u003cp\u003eCorrelation Versus Causation 265\u003c\/p\u003e \u003cp\u003eExercises Section 7.3 (23–42) 266\u003c\/p\u003e \u003cp\u003e7.4 Properties of Linear Combinations 267\u003c\/p\u003e \u003cp\u003eExpected Value and Variance of a Linear Combination 268\u003c\/p\u003e \u003cp\u003eThe PDF of a Sum 271\u003c\/p\u003e \u003cp\u003eMoment Generating Functions of Linear Combinations 273\u003c\/p\u003e \u003cp\u003eExercises Section 7.4 (43–65) 275\u003c\/p\u003e \u003cp\u003e7.5 The Central Limit Theorem and the Law of Large Numbers 278\u003c\/p\u003e \u003cp\u003eRandom Samples 278\u003c\/p\u003e \u003cp\u003eThe Central Limit Theorem 282\u003c\/p\u003e \u003cp\u003eA More General Central Limit Theorem 286\u003c\/p\u003e \u003cp\u003eOther Applications of the Central Limit Theorem 287\u003c\/p\u003e \u003cp\u003eThe Law of Large Numbers 288\u003c\/p\u003e \u003cp\u003eProof of the Central Limit Theorem 290\u003c\/p\u003e \u003cp\u003eExercises Section 7.5 (66–82) 290\u003c\/p\u003e \u003cp\u003e7.6 Simulation of Joint Probability Distributions 293\u003c\/p\u003e \u003cp\u003eSimulating Values from a Joint PMF 293\u003c\/p\u003e \u003cp\u003eSimulating Values from a Joint PDF 295\u003c\/p\u003e \u003cp\u003eExercises Section 7.6 (83–90) 297\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (91–124) 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Joint Probability Distributions:additional Topics 304\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 304\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Conditional Distributions and Expectation 304\u003c\/p\u003e \u003cp\u003eConditional Distributions and Independence 306\u003c\/p\u003e \u003cp\u003eConditional Expectation and Variance 307\u003c\/p\u003e \u003cp\u003eThe Laws of Total Expectation and Variance 308\u003c\/p\u003e \u003cp\u003eExercises Section 8.1 (1–18) 313\u003c\/p\u003e \u003cp\u003e8.2 The Bivariate Normal Distribution 315\u003c\/p\u003e \u003cp\u003eConditional Distributions of X and Y 317\u003c\/p\u003e \u003cp\u003eRegression to the Mean 318\u003c\/p\u003e \u003cp\u003eThe Multivariate Normal Distribution 319\u003c\/p\u003e \u003cp\u003eBivariate Normal Calculations with Software 319\u003c\/p\u003e \u003cp\u003eExercises Section 8.2 (19–30) 320\u003c\/p\u003e \u003cp\u003e8.3 Transformations of Jointly Distributed Random Variables 321\u003c\/p\u003e \u003cp\u003eThe Joint Distribution of Two New Random Variables 322\u003c\/p\u003e \u003cp\u003eThe Distribution of a Single New RV 323\u003c\/p\u003e \u003cp\u003eThe Joint Distribution of More Than Two New Variables 325\u003c\/p\u003e \u003cp\u003eExercises Section 8.3 (31–38) 326\u003c\/p\u003e \u003cp\u003e8.4 Reliability 327\u003c\/p\u003e \u003cp\u003eThe Reliability Function 327\u003c\/p\u003e \u003cp\u003eSeries and Parallel System Designs 329\u003c\/p\u003e \u003cp\u003eMean Time to Failure 331\u003c\/p\u003e \u003cp\u003eThe Hazard Function 332\u003c\/p\u003e \u003cp\u003eExercises Section 8.4 (39–50) 335\u003c\/p\u003e \u003cp\u003e8.5 Order Statistics 337\u003c\/p\u003e \u003cp\u003eThe Distributions of Y\u003csub\u003en\u003c\/sub\u003e and Y\u003csub\u003e1\u003c\/sub\u003e  337\u003c\/p\u003e \u003cp\u003eThe Distribution of the ith Order Statistic 339\u003c\/p\u003e \u003cp\u003eThe Joint Distribution of All n Order Statistics 340\u003c\/p\u003e \u003cp\u003eExercises Section 8.5 (51–60) 342\u003c\/p\u003e \u003cp\u003e8.6 Further Simulation Tools for Jointly Distributed Random Variables 343\u003c\/p\u003e \u003cp\u003eThe Conditional Distribution Method of Simulation 343\u003c\/p\u003e \u003cp\u003eSimulating a Bivariate Normal Distribution 344\u003c\/p\u003e \u003cp\u003eSimulation Methods for Reliability 346\u003c\/p\u003e \u003cp\u003eExercises Section 8.6 (61–68) 347\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (69–82) 348\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 the Basics of Statistical Inference 351\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 351\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Point Estimation 351\u003c\/p\u003e \u003cp\u003eEstimates and Estimators 352\u003c\/p\u003e \u003cp\u003eAssessing Estimators: Accuracy and Precision 354\u003c\/p\u003e \u003cp\u003eExercises Section 9.1 (1–18) 357\u003c\/p\u003e \u003cp\u003e9.2 Maximum Likelihood Estimation 360\u003c\/p\u003e \u003cp\u003eSome Properties of MLEs 366\u003c\/p\u003e \u003cp\u003eExercises Section 9.2 (19–30) 367\u003c\/p\u003e \u003cp\u003e9.3 Statistical Intervals 368\u003c\/p\u003e \u003cp\u003eConstructing a Confidence Interval 369\u003c\/p\u003e \u003cp\u003eConfidence Intervals for a Population Proportion 369\u003c\/p\u003e \u003cp\u003eConfidence Intervals for a Population Mean 371\u003c\/p\u003e \u003cp\u003eFurther Comments on Statistical Intervals 375\u003c\/p\u003e \u003cp\u003eConfidence Intervals with Software 375\u003c\/p\u003e \u003cp\u003eExercises Section 9.3 (31–48) 376\u003c\/p\u003e \u003cp\u003e9.4 Hypothesis Tests 379\u003c\/p\u003e \u003cp\u003eHypotheses and Test Procedures 380\u003c\/p\u003e \u003cp\u003eHypothesis Testing for a Population Mean 381\u003c\/p\u003e \u003cp\u003eErrors in Hypothesis Testing and the Power of a Test 385\u003c\/p\u003e \u003cp\u003eHypothesis Testing for a Population Proportion 388\u003c\/p\u003e \u003cp\u003eSoftware for Hypothesis Test Calculations 389\u003c\/p\u003e \u003cp\u003eExercises Section 9.4 (49–71) 391\u003c\/p\u003e \u003cp\u003e9.5 Bayesian Estimation 393\u003c\/p\u003e \u003cp\u003eThe Posterior Distribution of a Parameter 394\u003c\/p\u003e \u003cp\u003eInferences from the Posterior Distribution 397\u003c\/p\u003e \u003cp\u003eFurther Comments on Bayesian Inference 398\u003c\/p\u003e \u003cp\u003eExercises Section 9.5 (72–80) 399\u003c\/p\u003e \u003cp\u003e9.6 Simulation-Based Inference 400\u003c\/p\u003e \u003cp\u003eThe Bootstrap Method 400\u003c\/p\u003e \u003cp\u003eInterval Estimation Using the Bootstrap 402\u003c\/p\u003e \u003cp\u003eHypothesis Tests Using the Bootstrap 404\u003c\/p\u003e \u003cp\u003eMore on Simulation-Based Inference 405\u003c\/p\u003e \u003cp\u003eExercises Section 9.6 (81–90) 405\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (91–116) 407\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Markov Chains 411\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 411\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Terminology and Basic Properties 411\u003c\/p\u003e \u003cp\u003eThe Markov Property 413\u003c\/p\u003e \u003cp\u003eExercises Section 10.1 (1–10) 416\u003c\/p\u003e \u003cp\u003e10.2 The Transition Matrix and the Chapman–Kolmogorov Equations 418\u003c\/p\u003e \u003cp\u003eThe Transition Matrix 418\u003c\/p\u003e \u003cp\u003eComputation of Multistep Transition Probabilities 419\u003c\/p\u003e \u003cp\u003eExercises Section 10.2 (11–22) 423\u003c\/p\u003e \u003cp\u003e10.3 Specifying an Initial Distribution 426\u003c\/p\u003e \u003cp\u003eA Fixed Initial State 428\u003c\/p\u003e \u003cp\u003eExercises Section 10.3 (23–30) 429\u003c\/p\u003e \u003cp\u003e10.4 Regular Markov Chains and the Steady-State Theorem 430\u003c\/p\u003e \u003cp\u003eRegular Chains 431\u003c\/p\u003e \u003cp\u003eThe Steady-State Theorem 432\u003c\/p\u003e \u003cp\u003eInterpreting the Steady-State Distribution 433\u003c\/p\u003e \u003cp\u003eEfficient Computation of Steady-State Probabilities 435\u003c\/p\u003e \u003cp\u003eIrreducible and Periodic Chains 437\u003c\/p\u003e \u003cp\u003eExercises Section 10.4 (31–43) 438\u003c\/p\u003e \u003cp\u003e10.5 Markov Chains with Absorbing States 440\u003c\/p\u003e \u003cp\u003eTime to Absorption 441\u003c\/p\u003e \u003cp\u003eMean Time to Absorption 444\u003c\/p\u003e \u003cp\u003eMean First Passage Times 448\u003c\/p\u003e \u003cp\u003eProbabilities of Eventual Absorption 449\u003c\/p\u003e \u003cp\u003eExercises Section 10.5 (44–58) 451\u003c\/p\u003e \u003cp\u003e10.6 Simulation of Markov Chains 453\u003c\/p\u003e \u003cp\u003eExercises Section 10.6 (59–66) 459\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (67–82) 461\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Random Processes 465\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 465\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Types of Random Processes 465\u003c\/p\u003e \u003cp\u003eClassification of Processes 468\u003c\/p\u003e \u003cp\u003eRandom Processes and Their Associated Random Variables 469\u003c\/p\u003e \u003cp\u003eExercises Section 11.1 (1–10) 470\u003c\/p\u003e \u003cp\u003e11.2 Properties of the Ensemble: Mean and Autocorrelation Functions 471\u003c\/p\u003e \u003cp\u003eMean and Variance Functions 471\u003c\/p\u003e \u003cp\u003eAutocovariance and Autocorrelation Functions 475\u003c\/p\u003e \u003cp\u003eThe Joint Distribution of Two Random Processes 477\u003c\/p\u003e \u003cp\u003eExercises Section 11.2 (11–24) 478\u003c\/p\u003e \u003cp\u003e11.3 Stationary and Wide-Sense Stationary Processes 479\u003c\/p\u003e \u003cp\u003eProperties of WSS Processes 483\u003c\/p\u003e \u003cp\u003eErgodic Processes 486\u003c\/p\u003e \u003cp\u003eExercises Section 11.3 (25–40) 488\u003c\/p\u003e \u003cp\u003e11.4 Discrete-Time Random Processes 489\u003c\/p\u003e \u003cp\u003eSpecial Discrete Sequences 491\u003c\/p\u003e \u003cp\u003eExercises Section 11.4 (41–52) 493\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (53–64) 494\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Families of Random Processes 497\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 497\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Poisson Processes 497\u003c\/p\u003e \u003cp\u003eRelation to Exponential and Gamma Distributions 499\u003c\/p\u003e \u003cp\u003eCombining and Decomposing Poisson Processes 502\u003c\/p\u003e \u003cp\u003eAlternative Definition of a Poisson Process 504\u003c\/p\u003e \u003cp\u003eNonhomogeneous Poisson Processes 505\u003c\/p\u003e \u003cp\u003eThe Poisson Telegraphic Process 506\u003c\/p\u003e \u003cp\u003eExercises Section 12.1 (1–18) 507\u003c\/p\u003e \u003cp\u003e12.2 Gaussian Processes 509\u003c\/p\u003e \u003cp\u003eBrownian Motion 510\u003c\/p\u003e \u003cp\u003eBrownian Motion as a Limit 512\u003c\/p\u003e \u003cp\u003eFurther Properties of Brownian Motion 512\u003c\/p\u003e \u003cp\u003eVariations on Brownian Motion 514\u003c\/p\u003e \u003cp\u003eExercises Section 12.2 (19–28) 515\u003c\/p\u003e \u003cp\u003e12.3 Continuous-Time Markov Chains 516\u003c\/p\u003e \u003cp\u003eInfinitesimal Parameters and Instantaneous Transition Rates 518\u003c\/p\u003e \u003cp\u003eSojourn Times and Transitions 520\u003c\/p\u003e \u003cp\u003eLong-Run Behavior of Continuous-Time Markov Chains 523\u003c\/p\u003e \u003cp\u003eExplicit Form of the Transition Matrix 526\u003c\/p\u003e \u003cp\u003eExercises Section 12.3 (29–40) 527\u003c\/p\u003e \u003cp\u003eSupplementary Exercises (41–51) 529\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Introduction to Signal Processing 532\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIntroduction 532\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Power Spectral Density 532\u003c\/p\u003e \u003cp\u003eExpected Power and the Power Spectral Density 532\u003c\/p\u003e \u003cp\u003eProperties of the Power Spectral Density 535\u003c\/p\u003e \u003cp\u003ePower in a Frequency Band 538\u003c\/p\u003e \u003cp\u003eWhite Noise Processes 539\u003c\/p\u003e \u003cp\u003eCross-Power Spectral Density for Two Processes 541\u003c\/p\u003e \u003cp\u003eExercises Section 13.1 (1–21) 542\u003c\/p\u003e \u003cp\u003e13.2 Random Processes and LTI Systems 544\u003c\/p\u003e \u003cp\u003eProperties of the LTI System Output 545\u003c\/p\u003e \u003cp\u003eIdeal Filters 548\u003c\/p\u003e \u003cp\u003eSignal Plus Noise 551\u003c\/p\u003e \u003cp\u003eExercises Section 13.2 (22–38) 554\u003c\/p\u003e \u003cp\u003e13.3 Discrete-Time Signal Processing 556\u003c\/p\u003e \u003cp\u003eRandom Sequences and LTI Systems 558\u003c\/p\u003e \u003cp\u003eSampling Random Sequences 560\u003c\/p\u003e \u003cp\u003eExercises Section 13.3 (39–50) 562\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Statistical Tables A- 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA. 1 Binomial CDF A- 1\u003c\/p\u003e \u003cp\u003eA. 2 Poisson CDF A- 4\u003c\/p\u003e \u003cp\u003eA. 3 Standard Normal CDF A- 5\u003c\/p\u003e \u003cp\u003eA. 4 Incomplete Gamma Function A- 7\u003c\/p\u003e \u003cp\u003eA. 5 Critical Values for t Distributions A- 7\u003c\/p\u003e \u003cp\u003eA. 6 Tail Areas of t Distributions A- 9\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Background Mathematics A- 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB. 1 Trigonometric Identities A- 13\u003c\/p\u003e \u003cp\u003eB. 2 Special Engineering Functions A- 13\u003c\/p\u003e \u003cp\u003eB. 3 o(h) Notation A- 14\u003c\/p\u003e \u003cp\u003eB. 4 The Delta Function A- 14\u003c\/p\u003e \u003cp\u003eB. 5 Fourier Transforms A- 15\u003c\/p\u003e \u003cp\u003eB. 6 Discrete-Time Fourier Transforms A- 16\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Important Probability Distributions A- 18\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC. 1 Discrete Distributions A- 18\u003c\/p\u003e \u003cp\u003eC. 2 Continuous Distributions A- 20\u003c\/p\u003e \u003cp\u003eC. 3 Matlab and R Commands A- 23\u003c\/p\u003e \u003cp\u003eBibliography B- 1\u003c\/p\u003e \u003cp\u003eAnswers to Odd-numbered Exercises S- 1\u003c\/p\u003e \u003cp\u003eIndex I- 1 \u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989858238693,"sku":"NP9781119717867","price":104.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119717867.jpg?v=1761785699","url":"https:\/\/k12savings.com\/es\/products\/probability-with-stem-applications-isbn-9781119717867","provider":"K12savings","version":"1.0","type":"link"}