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 Statistics was 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. |
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accept actually assume B₁ balls Bayes binomial called chosen Consider constant contains continuous decision defective defined degrees of freedom denote depend derived described determine discussion distribution with mean distribution with parameters drug equal estimator Example exist expectation experiment Find follows form a random function Furthermore given H₁ Hence hypotheses independent interval joint p.d.f. known least level of significance likelihood linear loss method normal distribution observed values obtained otherwise outcomes pairs particular person positive posterior Pr(X prior distribution probability problem properties random sample random variable rejected relation result sample mean satisfied sequence Show shown simple specified squares statistic sufficient statistic Suppose Suppose that X1 Table taken test procedure Theorem tion true unbiased estimator uniform distribution unknown Var(X variables X1 variance vector X₁ Y₁