Rinaldo B. Schinazi

Probability with Statistical Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book is intended as a one-semester first course in probability and statistics, requiring only a knowledge of calculus. It will be useful for students majoring in a number of disciplines:for example,biology, computer science, electrical engineer ing, mathematics, and physics. Many good texts in probability and statistics are intended for a one-year course and consist of a large number of topics. In this book, the number of topics is dras tically reduced. We concentrate instead on several important concepts that every student should understand and be able to apply in an interesting and useful way. Thus statistics is introduced at an early stage. The presentation focuses on topics in probability and statistics and tries to min imize the difficulties students often have with calculus. Theory therefore is kept to a minimum and interesting examples are provided throughout. Chapter I contains the basic rules of probability and conditional probability with some interesting ap plications such asBayes' rule and the birthday problem. In Chapter 2 discrete and continuous random variables, expectation and variance are introduced. This chapter is mostly computational with a few probability concepts and many applications of calculus. In Chapters 3 and 4 we get to the heart of the subject: binomial distribu tion, normal approximation of the binomial, Poisson distribution, the Law of Large Numbers and the Central Limit Theorem. Wealso cover the Poisson approximation of the binomial (in a nonstandard way) and the Poisson scattering theorem.

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 219
• Erscheinungstermin: 9. März 2013
• Englisch
• ISBN-13: 9781475734218
• Artikelnr.: 44204294

Autorenporträt

Rinaldo Schinazi is a professor at the University of Colorado Springs. He teaches a wide range of probability and statistics courses. His research is in probability models for population biology.

Inhaltsangabe

Probability Space.- Conditional probabilities.- Discrete random variables.- Binomial random variables.- Poisson random variables.- Simulations of discrete random variables.- Combinatorics.- Continuous random variables.- The sample average and sample.- Estimating and testing proportions.- Estimating and testing means.- Small samples.- Chi-squared tests.- Design of experiments.- The cumulative distribution function.- Continuous joint distributions.- Covariance and independence.- Conditional distribution and expectation.- The bivariate normal distribution.- Sums of Bernoulli random variables.- Coupling random variables.- The moment generating function.- The chi-squared, Student and F distributions.- Sampling from a normal distribution.- Finding estimators.- Comparing estimators.- Best unbiased estimators.- Bayes' estimator.- Multiple linear regression.- List of common discrete distributions.- List of common continuous distributions.- Further reading.- Normal table.- Student table.- Chi-squared table.- Index.