{"product_id":"probability-9781118241257","title":"Probability","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAn introduction to probability at the undergraduate level     Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xiv\u003c\/p\u003e \u003cp\u003eIntroduction xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 First Principles 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Random Experiment, Sample Space, Event 1\u003c\/p\u003e \u003cp\u003e1.2 What Is a Probability? 3\u003c\/p\u003e \u003cp\u003e1.3 Probability Function 4\u003c\/p\u003e \u003cp\u003e1.4 Properties of Probabilities 7\u003c\/p\u003e \u003cp\u003e1.5 Equally Likely Outcomes 10\u003c\/p\u003e \u003cp\u003e1.6 Counting I 12\u003c\/p\u003e \u003cp\u003e1.7 Problem-Solving Strategies: Complements, Inclusion–Exclusion 14\u003c\/p\u003e \u003cp\u003e1.8 Random Variables 18\u003c\/p\u003e \u003cp\u003e1.9 A Closer Look at Random Variables 21\u003c\/p\u003e \u003cp\u003e1.10 A First Look at Simulation 22\u003c\/p\u003e \u003cp\u003e1.11 Summary 26\u003c\/p\u003e \u003cp\u003eExercises 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Conditional Probability 34\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Conditional Probability 34\u003c\/p\u003e \u003cp\u003e2.2 New Information Changes the Sample Space 39\u003c\/p\u003e \u003cp\u003e2.3 Finding P(A and B) 40\u003c\/p\u003e \u003cp\u003e2.4 Conditioning and the Law of Total Probability 49\u003c\/p\u003e \u003cp\u003e2.5 Bayes Formula and Inverting a Conditional Probability 57\u003c\/p\u003e \u003cp\u003e2.6 Summary 61\u003c\/p\u003e \u003cp\u003eExercises 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Independence and Independent Trials 68\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Independence and Dependence 68\u003c\/p\u003e \u003cp\u003e3.2 Independent Random Variables 76\u003c\/p\u003e \u003cp\u003e3.3 Bernoulli Sequences 77\u003c\/p\u003e \u003cp\u003e3.4 Counting II 79\u003c\/p\u003e \u003cp\u003e3.5 Binomial Distribution 88\u003c\/p\u003e \u003cp\u003e3.6 Stirling’s Approximation 95\u003c\/p\u003e \u003cp\u003e3.7 Poisson Distribution 96\u003c\/p\u003e \u003cp\u003e3.8 Product Spaces 105\u003c\/p\u003e \u003cp\u003e3.9 Summary 107\u003c\/p\u003e \u003cp\u003eExercises 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Random Variables 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Expectation 118\u003c\/p\u003e \u003cp\u003e4.2 Functions of Random Variables 121\u003c\/p\u003e \u003cp\u003e4.3 Joint Distributions 125\u003c\/p\u003e \u003cp\u003e4.4 Independent Random Variables 130\u003c\/p\u003e \u003cp\u003e4.5 Linearity of Expectation 135\u003c\/p\u003e \u003cp\u003e4.6 Variance and Standard Deviation 140\u003c\/p\u003e \u003cp\u003e4.7 Covariance and Correlation 149\u003c\/p\u003e \u003cp\u003e4.8 Conditional Distribution 156\u003c\/p\u003e \u003cp\u003e4.9 Properties of Covariance and Correlation 162\u003c\/p\u003e \u003cp\u003e4.10 Expectation of a Function of a Random Variable 164\u003c\/p\u003e \u003cp\u003e4.11 Summary 165\u003c\/p\u003e \u003cp\u003eExercises 168\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 A Bounty of Discrete Distributions 176\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Geometric Distribution 176\u003c\/p\u003e \u003cp\u003e5.2 Negative Binomial—Up from the Geometric 184\u003c\/p\u003e \u003cp\u003e5.3 Hypergeometric—Sampling Without Replacement 189\u003c\/p\u003e \u003cp\u003e5.4 From Binomial to Multinomial 194\u003c\/p\u003e \u003cp\u003e5.5 Benford’s Law 201\u003c\/p\u003e \u003cp\u003e5.6 Summary 203\u003c\/p\u003e \u003cp\u003eExercises 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Continuous Probability 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Probability Density Function 213\u003c\/p\u003e \u003cp\u003e6.2 Cumulative Distribution Function 216\u003c\/p\u003e \u003cp\u003e6.3 Uniform Distribution 220\u003c\/p\u003e \u003cp\u003e6.4 Expectation and Variance 222\u003c\/p\u003e \u003cp\u003e6.5 Exponential Distribution 224\u003c\/p\u003e \u003cp\u003e6.6 Functions of Random Variables I 229\u003c\/p\u003e \u003cp\u003e6.7 Joint Distributions 235\u003c\/p\u003e \u003cp\u003e6.8 Independence 243\u003c\/p\u003e \u003cp\u003e6.9 Covariance, Correlation 249\u003c\/p\u003e \u003cp\u003e6.10 Functions of Random Variables II 251\u003c\/p\u003e \u003cp\u003e6.11 Geometric Probability 256\u003c\/p\u003e \u003cp\u003e6.12 Summary 262\u003c\/p\u003e \u003cp\u003eExercises 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Continuous Distributions 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Normal Distribution 273\u003c\/p\u003e \u003cp\u003e7.2 Gamma Distribution 290\u003c\/p\u003e \u003cp\u003e7.3 Poisson Process 296\u003c\/p\u003e \u003cp\u003e7.4 Beta Distribution 304\u003c\/p\u003e \u003cp\u003e7.5 Pareto Distribution, Power Laws, and the 80-20 Rule 308\u003c\/p\u003e \u003cp\u003e7.6 Summary 312\u003c\/p\u003e \u003cp\u003eExercises 315\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Conditional Distribution, Expectation, and Variance 322\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Conditional Distributions 322\u003c\/p\u003e \u003cp\u003e8.2 Discrete and Continuous: Mixing it up 328\u003c\/p\u003e \u003cp\u003e8.3 Conditional Expectation 332\u003c\/p\u003e \u003cp\u003e8.4 Computing Probabilities by Conditioning 342\u003c\/p\u003e \u003cp\u003e8.5 Conditional Variance 346\u003c\/p\u003e \u003cp\u003e8.6 Summary 352\u003c\/p\u003e \u003cp\u003eExercises 353\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Limits 359\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Weak Law of Large Numbers 361\u003c\/p\u003e \u003cp\u003e9.2 Strong Law of Large Numbers 367\u003c\/p\u003e \u003cp\u003e9.3 Monte Carlo Integration 372\u003c\/p\u003e \u003cp\u003e9.4 Central Limit Theorem 376\u003c\/p\u003e \u003cp\u003e9.5 Moment-Generating Functions 385\u003c\/p\u003e \u003cp\u003e9.6 Summary 391\u003c\/p\u003e \u003cp\u003eExercises 392\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Additional Topics 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Bivariate Normal Distribution 399\u003c\/p\u003e \u003cp\u003e10.2 Transformations of Two Random Variables 407\u003c\/p\u003e \u003cp\u003e10.3 Method of Moments 411\u003c\/p\u003e \u003cp\u003e10.4 Random Walk on Graphs 413\u003c\/p\u003e \u003cp\u003e10.5 Random Walks on Weighted Graphs and Markov Chains 421\u003c\/p\u003e \u003cp\u003e10.6 From Markov Chain to Markov Chain Monte Carlo 429\u003c\/p\u003e \u003cp\u003e10.7 Summary 440\u003c\/p\u003e \u003cp\u003eExercises 442\u003c\/p\u003e \u003cp\u003eAppendix A Getting Started with R 447\u003c\/p\u003e \u003cp\u003eAppendix B Probability Distributions in R 458\u003c\/p\u003e \u003cp\u003eAppendix C Summary of Probability Distributions 459\u003c\/p\u003e \u003cp\u003eAppendix D Reminders from Algebra and Calculus 462\u003c\/p\u003e \u003cp\u003eAppendix E More Problems for Practice 464\u003c\/p\u003e \u003cp\u003eSolutions to Exercises 469\u003c\/p\u003e \u003cp\u003eReferences 487\u003c\/p\u003e \u003cp\u003eIndex 491\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406843060567,"sku":"9781118241257","price":107.06,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118241257.jpg?v=1730497310","url":"https:\/\/bookcurl.com\/products\/probability-9781118241257","provider":"Book Curl","version":"1.0","type":"link"}