This concise text is intended for a one-semester course, and offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications.
This concise text is intended for a one-semester course, and offers a practical introduction to probability for undergraduates at all levels with different backgrounds and views towards applications.
Schinazi, R., University of Colorado, Colorado Springs, USA
Inhaltsangabe
Preface Probability Space Random Variables Binomial and Poisson Random Variables Limit Theorems Estimation and Hypothesis Testing Linear Regression Moment Generating Functions Transformations of Random Variables and Random Vectors Appendices Index
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.
Preface Probability Space Random Variables Binomial and Poisson Random Variables Limit Theorems Estimation and Hypothesis Testing Linear Regression Moment Generating Functions Transformations of Random Variables and Random Vectors Appendices Index
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.
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