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Introduction to Probability, Second Edition

Introduction to Probability, Second Edition

Autorzy
Wydawnictwo Taylor & Francis Ltd
Data wydania 08/02/2019
Liczba stron 620
Forma publikacji książka w twardej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
Język angielski
ISBN 9781138369917
Kategorie Prawdopodobieństwo i statystyka
418.95 PLN (z VAT)
$94.24 / €89.82 / £77.97 /
Produkt na zamówienie
Dostawa 3-4 tygodnie
Ilość
Do schowka

Opis książki

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory.
The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces.

The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.


The second edition adds many new examples, exercises, and explanations, to deepen understanding of the ideas, clarify subtle concepts, and respond to feedback from many students and readers. New supplementary online resources have been developed, including animations and interactive visualizations, and the book has been updated to dovetail with these resources.


Supplementary material is available on Joseph Blitzstein's website www. stat110.net. The supplements include:
Solutions to selected exercises
Additional practice problems
Handouts including review material and sample exams Animations and interactive visualizations created in connection with the edX online version of Stat 110.
Links to lecture videos available on ITunes U and YouTube There is also a complete instructor's solutions manual available to instructors who require the book for a course.

Introduction to Probability, Second Edition

Spis treści

Probability and Counting

Why study probability?





Sample spaces and Pebble World





Naive definition of probability





How to count





Story proofs





Non-naive definition of probability





Recap





R





Exercises



















Conditional Probability







The importance of thinking conditionally





Definition and intuition





Bayes' rule and the law of total probability





Conditional probabilities are probabilities





Independence of events





Coherency of Bayes' rule





Conditioning as a problem-solving tool





Pitfalls and paradoxes





Recap





R





Exercises



















Random Variables and Their Distributions







Random variables





Distributions and probability mass functions





Bernoulli and Binomial





Hypergeometric





Discrete Uniform





Cumulative distribution functions





Functions of random variables





Independence of rvs





Connections between Binomial and Hypergeometric





Recap





R





Exercises



















Expectation







Definition of expectation





Linearity of expectation





Geometric and Negative Binomial





Indicator rvs and the fundamental bridge





Law of the unconscious statistician (LOTUS)





Variance





Poisson





Connections between Poisson and Binomial





*Using probability and expectation to prove existence





Recap





R





Exercises



















Continuous Random Variables







Probability density functions





Uniform





Universality of the Uniform





Normal





Exponential





Poisson processes





Symmetry of iid continuous rvs





Recap





R





Exercises



















Moments







Summaries of a distribution





Interpreting moments





Sample moments





Moment generating functions





Generating moments with MGFs





Sums of independent rvs via MGFs





*Probability generating functions





Recap





R





Exercises



















Joint Distributions







Joint, marginal, and conditional





D LOTUS





Covariance and correlation





Multinomial





Multivariate Normal





Recap





R





Exercises



















Transformations







Change of variables





Convolutions





Beta





Gamma





Beta-Gamma connections





Order statistics





Recap





R





Exercises



















Conditional Expectation







Conditional expectation given an event





Conditional expectation given an rv





Properties of conditional expectation





*Geometric interpretation of conditional expectation





Conditional variance





Adam and Eve examples





Recap





R





Exercises



















Inequalities and Limit Theorems







Inequalities





Law of large numbers





Central limit theorem





Chi-Square and Student-t





Recap





R





Exercises



















Markov Chains







Markov property and transition matrix





Classification of states





Stationary distribution





Reversibility





Recap





R





Exercises



















Markov Chain Monte Carlo







Metropolis-Hastings





Recap





R





Exercises



















Poisson Processes











Poisson processes in one dimension





Conditioning, superposition, thinning





Poisson processes in multiple dimensions





Recap





R





Exercises











A Math





A Sets





A Functions





A Matrices





A Difference equations





A Differential equations





A Partial derivatives





A Multiple integrals





A Sums





A Pattern recognition





A Common sense and checking answers











B R





B Vectors





B Matrices





B Math





B Sampling and simulation





B Plotting





B Programming





B Summary statistics





B Distributions





C Table of distributions











Bibliography





Index

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