LEADER 05758nam 2200841Ia 450 001 9910141253303321 005 20170815105350.0 010 $a9786613622280 010 $a9781280592454 010 $a1280592451 010 $a9781118231296 010 $a1118231295 010 $a9781118231302 010 $a1118231309 035 $a(CKB)2670000000177369 035 $a(EBL)822093 035 $a(SSID)ssj0000640080 035 $a(PQKBManifestationID)11439461 035 $a(PQKBTitleCode)TC0000640080 035 $a(PQKBWorkID)10611367 035 $a(PQKB)10064348 035 $a(MiAaPQ)EBC822093 035 $a(PPN)170233332 035 $a(OCoLC)795795373 035 $a(FR-PaCSA)88808467 035 $a(CaSebORM)9781118231326 035 $a(OCoLC)814403702 035 $a(OCoLC)ocn814403702 035 $a(FRCYB88808467)88808467 035 $a(Perlego)1011013 035 $a(EXLCZ)992670000000177369 100 $a20111025d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aProbability, statistics, and stochastic processes /$fPeter Olofsson, Mikael Andersson 205 $a2nd ed. 210 $aHoboken, N.J. $cWiley$d2012 215 $a1 online resource (574 p.) 300 $aIncludes index. 311 08$a9781118231326 311 08$a1118231325 311 08$a9780470889749 311 08$a0470889748 320 $aIncludes bibliographical references and index. 327 $aPROBABILITY, STATISTICS, AND STOCHASTIC PROCESSES; CONTENTS; Preface; Preface to the First Edition; 1 Basic Probability Theory; 1.1 Introduction; 1.2 Sample Spaces and Events; 1.3 The Axioms of Probability; 1.4 Finite Sample Spaces and Combinatorics; 1.4.1 Combinatorics; 1.5 Conditional Probability and Independence; 1.5.1 Independent Events; 1.6 The Law of Total Probability and Bayes' Formula; 1.6.1 Bayes' Formula; 1.6.2 Genetics and Probability; 1.6.3 Recursive Methods; Problems; 2 Random Variables; 2.1 Introduction; 2.2 Discrete Random Variables; 2.3 Continuous Random Variables 327 $a2.3.1 The Uniform Distribution2.3.2 Functions of Random Variables; 2.4 Expected Value and Variance; 2.4.1 The Expected Value of a Function of a Random Variable; 2.4.2 Variance of a Random Variable; 2.5 Special Discrete Distributions; 2.5.1 Indicators; 2.5.2 The Binomial Distribution; 2.5.3 The Geometric Distribution; 2.5.4 The Poisson Distribution; 2.5.5 The Hypergeometric Distribution; 2.5.6 Describing Data Sets; 2.6 The Exponential Distribution; 2.7 The Normal Distribution; 2.8 Other Distributions; 2.8.1 The Lognormal Distribution; 2.8.2 The Gamma Distribution; 2.8.3 The Cauchy Distribution 327 $a2.8.4 Mixed Distributions2.9 Location Parameters; 2.10 The Failure Rate Function; 2.10.1 Uniqueness of the Failure Rate Function; Problems; 3 Joint Distributions; 3.1 Introduction; 3.2 The Joint Distribution Function; 3.3 Discrete Random Vectors; 3.4 Jointly Continuous Random Vectors; 3.5 Conditional Distributions and Independence; 3.5.1 Independent Random Variables; 3.6 Functions of Random Vectors; 3.6.1 Real-Valued Functions of Random Vectors; 3.6.2 The Expected Value and Variance of a Sum; 3.6.3 Vector-Valued Functions of Random Vectors; 3.7 Conditional Expectation 327 $a3.7.1 Conditional Expectation as a Random Variable3.7.2 Conditional Expectation and Prediction; 3.7.3 Conditional Variance; 3.7.4 Recursive Methods; 3.8 Covariance and Correlation; 3.8.1 The Correlation Coefficient; 3.9 The Bivariate Normal Distribution; 3.10 Multidimensional Random Vectors; 3.10.1 Order Statistics; 3.10.2 Reliability Theory; 3.10.3 The Multinomial Distribution; 3.10.4 The Multivariate Normal Distribution; 3.10.5 Convolution; 3.11 Generating Functions; 3.11.1 The Probability Generating Function; 3.11.2 The Moment Generating Function; 3.12 The Poisson Process 327 $a3.12.1 Thinning and SuperpositionProblems; 4 Limit Theorems; 4.1 Introduction; 4.2 The Law of Large Numbers; 4.3 The Central Limit Theorem; 4.3.1 The Delta Method; 4.4 Convergence in Distribution; 4.4.1 Discrete Limits; 4.4.2 Continuous Limits; Problems; 5 Simulation; 5.1 Introduction; 5.2 Random Number Generation; 5.3 Simulation of Discrete Distributions; 5.4 Simulation of Continuous Distributions; 5.5 Miscellaneous; Problems; 6 Statistical Inference; 6.1 Introduction; 6.2 Point Estimators; 6.2.1 Estimating the Variance; 6.3 Confidence Intervals 327 $a6.3.1 Confidence Interval for the Mean in the Normal Distribution with Known Variance 330 $a Praise for the First Edition "". . . an excellent textbook . . . well organized and neatly written.""-Mathematical Reviews "". . . amazingly interesting . . .""-Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introdu 606 $aStochastic processes$vTextbooks 606 $aProbabilities$vTextbooks 606 $aMathematical statistics$vTextbooks 615 0$aStochastic processes 615 0$aProbabilities 615 0$aMathematical statistics 676 $a519.2 676 $a519.2/3 676 $a519.23 686 $aMAT029000$2bisacsh 700 $aOlofsson$b Peter$f1963-$0315944 701 $aAndersson$b Mikael$0522136 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910141253303321 996 $aProbability, statistics, and stochastic processes$9835631 997 $aUNINA