Probability and StatisticsThe revision of this well-respected text presents a balanced approach of the classical and Bayesian methods and now includes a new chapter on simulation (including Markov chain Monte Carlo and the Bootstrap), expanded coverage of residual analysis in linear models, and more examples using real data. Probability & Statisticswas written for a one or two semester probability and statistics course offered primarily at four-year institutions and taken mostly by sophomore and junior level students, majoring in mathematics or statistics. Calculus is a prerequisite, and a familiarity with the concepts and elementary properties of vectors and matrices is a plus. Introduction to Probability; Conditional Probability; Random Variables and Distribution; Expectation; Special Distributions; Estimation; Sampling Distributions of Estimators; Testing Hypotheses; Categorical Data and Nonparametric Methods; Linear Statistical Models; Simulation For all readers interested in probability and statistics. |
Contents
Introduction to Probability | 1 |
Conditional Probability | 49 |
Random Variables and Distributions | 97 |
Copyright | |
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approximately assume B₁ Bayes estimator Bernoulli Bernoulli distribution beta distribution binomial distribution bootstrap calculate coefficient compute conditional distribution conditional p.d.f. conditions of Exercise confidence interval Consider continuous distribution defined degrees of freedom denote discrete distribution distribution with mean distribution with parameters event Example exponential distribution following hypotheses form a random gamma distribution given by Eq H₁ improper prior integral joint distribution joint p.d.f. level of significance linear Markov chain mean µ median null hypothesis observed values obtained outcomes Poisson distribution possible values posterior distribution posterior probability power function Pr(A Pr(B Pr(X Pr(Y prior distribution problem quantile random sample regression reject sample mean Section selected at random specified standard deviation standard normal distribution sufficient statistic Suppose that X1 Table test procedure Theorem unbiased estimator uniform distribution unknown Var(X variance o² X₁ x² distribution Y₁