Probability with applications and R / / Amy S. Wagaman, Robert P. Dobrow

• Record Nr.: UNINA9910555264603321
• Autore: Wagaman Amy S. <1982->
• Pubbl/distr/stampa: Hoboken, New Jersey : , : Wiley, , [2021]; ©2021
• ISBN: 1-5231-4377-0; 1-119-69241-5; 1-119-69243-1; 1-119-69234-2
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (547 pages)
• Disciplina: 519.502855133
• Soggetti: Probabilities - Data processing; Probabilities; R (Computer program language); Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Contents -- Preface -- Acknowledgments -- About the Companion Website -- Introduction -- Chapter 1 First Principles -- 1.1 Random Experiment, Sample Space, Event -- 1.2 What Is a Probability? -- 1.3 Probability Function -- 1.4 Properties of Probabilities -- 1.5 Equally likely outcomes -- 1.6 Counting I -- 1.6.1 Permutations -- 1.7 Counting II -- 1.7.1 Combinations and Binomial Coefficients -- 1.8 Problem‐Solving Strategies: Complements and Inclusion-Exclusion -- 1.9 A First Look at Simulation -- 1.10 Summary -- Exercises -- Chapter 2 Conditional Probability and Independence -- 2.1 Conditional Probability -- 2.2 New Information Changes the Sample Space -- 2.3 Finding P(A and B) -- 2.3.1 Birthday Problem -- 2.4 Conditioning and the Law of Total Probability -- 2.5 Bayes Formula and Inverting a Conditional Probability -- 2.6 Independence and Dependence -- 2.7 Product Spaces* -- 2.8 Summary -- Exercises -- Chapter 3 INTRODUCTION TO DISCRETE RANDOM VARIABLES -- Learning Outcomes -- 3.1 Random Variables -- 3.2 Independent Random ; Variables -- 3.3 Bernoulli Sequences -- 3.4 Binomial Distribution -- 3.5 Poisson Distribution -- 3.5.1 Poisson Approximation of Binomial Distribution -- 3.5.2 Poisson as Limit of Binomial Probabilities* -- 3.6 Summary -- Exercises -- Chapter 4 Expectation and More with Discrete Random Variables -- 4.1 Expectation -- 4.2 Functions of Random Variables -- 4.3 Joint distributions -- 4.4 Independent Random Variables -- 4.4.1 Sums of Independent Random Variables -- 4.5 Linearity of expectation -- 4.6 Variance and Standard Deviation -- 4.7 Covariance and Correlation -- 4.8 Conditional Distribution -- 4.8.1 Introduction to Conditional Expectation -- 4.9 Properties of Covariance and Correlation* -- 4.10 Expectation of a Function of a Random Variable* -- 4.11 Summary -- Exercises.; Chapter 5 More Discrete Distributions and Their Relationships -- 5.1 Geometric Distribution -- 5.1.1 Memorylessness -- 5.1.2 Coupon Collecting and Tiger Counting -- 5.2 Moment‐Generating Functions -- 5.3 Negative Binomial-Up from the Geometric -- 5.4 Hypergeometric-Sampling Without Replacement -- 5.5 From Binomial to Multinomial -- 5.6 Benford's Law* -- 5.7 Summary -- Exercises -- Chapter 6 Continuous Probability -- 6.1 Probability Density Function -- 6.2 Cumulative Distribution Function -- 6.3 Expectation and Variance -- 6.4 Uniform Distribution -- 6.5 Exponential Distribution -- 6.5.1 Memorylessness -- 6.6 Joint Distributions -- 6.7 Independence -- 6.7.1 Accept-Reject Method -- 6.8 Covariance, Correlation -- 6.9 Summary -- Exercises -- Chapter 7 Continuous Distributions -- 7.1 Normal Distribution -- 7.1.1 Standard Normal Distribution -- 7.1.2 Normal Approximation of Binomial Distribution -- 7.1.3 Quantiles -- 7.1.4 Sums of Independent Normals -- 7.2 Gamma Distribution -- 7.2.1 Probability as a Technique of Integration -- 7.3 Poisson Process -- 7.4 Beta Distribution -- 7.5 Pareto Distribution* -- 7.6 Summary -- Exercises -- Chapter 8 Densities of Functions of Random Variables -- 8.1 Densities via CDFs -- 8.1.1 Simulating a Continuous Random Variable -- 8.1.2 Method of Transformations -- 8.2 Maximums, Minimums, and Order Statistics -- 8.3 Convolution -- 8.4 Geometric Probability -- 8.5 Transformations of Two Random Variables* -- 8.6 Summary -- Exercises -- Chapter 9 Conditional Distribution, Expectation, and Variance -- 9.1 Conditional Distributions -- 9.2 DISCRETE AND CONTINUOUS: MIXING IT UP -- 9.3 CONDITIONAL EXPECTATION -- 9.3.1 From Function to Random Variable -- 9.3.2 Random Sum of Random Variables -- 9.4 COMPUTING PROBABILITIES BY CONDITIONING -- 9.5 CONDITIONAL VARIANCE -- 9.6 BIVARIATE NORMAL DISTRIBUTION* -- 9.7 SUMMARY -- Exercises.; Chapter 10 Limits -- 10.1 WEAK LAW OF LARGE NUMBERS -- 10.1.1 Markov and Chebyshev Inequalities -- 10.2 STRONG LAW OF LARGE NUMBERS -- 10.3 METHOD OF MOMENTS* -- 10.4 MONTE CARLO INTEGRATION -- 10.5 CENTRAL LIMIT THEOREM -- 10.5.1 Central Limit Theorem and Monte Carlo -- 10.6 A PROOF OF THE CENTRAL LIMIT THEOREM -- 10.7 SUMMARY -- Exercises -- Chapter 11 Beyond Random Walks And Markov Chains -- 11.1 RANDOM WALKS ON GRAPHS -- 11.1.1 Long‐Term Behavior -- 11.2 RANDOM WALKS ON WEIGHTED GRAPHS AND MARKOV CHAINS -- 11.2.1 Stationary Distribution -- 11.3 FROM MARKOV CHAIN TO MARKOV CHAIN MONTE CARLO -- 11.4 SUMMARY -- Exercises -- Chapter A Probability Distributions in R -- Chapter B Summary of Probability Distributions -- Chapter C Mathematical Reminders -- Chapter D Working with Joint Distributions -- SOLUTIONS TO EXERCISES -- References -- Index -- EULA.

Surgical Treatment of Pancreatic Ductal Adenocarcinoma

• Record Nr.: UNINA9910557364803321
• Autore: Satoi Sohei
• Pubbl/distr/stampa: Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2021
• Descrizione fisica: 1 online resource (214 p.)
• Soggetti: Medicine and Nursing; Surgery
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Sommario/riassunto: This book contains the art and science in current standards of surgical treatment of pancreatic ductal adenocarcinoma. It explains the clinical role of surgical resection during multimodal treatment in patients with pancreatic ductal adenocarcinoma, novel surgical techniques including extended pancreatectomy and minimally invasive surgery, risk of cancer in IPMN, and the clinical importance of liquid biopsy.