Probability and statistics
The 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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Introduction to Probability
Random Variables and Distributions
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9 is unknown assume balls Bayes estimator Bernoulli distribution beta distribution binomial distribution conditions of Exercise Consider continuous distribution degrees of freedom determine the probability determine the value discrete distribution distribution of 9 distribution with mean distribution with parameters estimator of 9 Example exponential distribution following hypotheses follows from Eq form a random Furthermore gamma distribution given in Eq given value H0 is true Hence integer joint distribution joint p.d.f. level of significance likelihood function linear loss function null hypothesis H0 observed values obtained outcomes parameter 9 Poisson distribution possible values posterior distribution Pr(A Pr(X prior distribution problem random sample random variables Xu rejecting H0 sample mean selected at random sequence significance a0 specified standard normal distribution statistician subset sufficient statistic Suppose that Xu Table test procedure Theorem tossed total number unbiased estimator uniform distribution value of 9 Var(X variance a2 x2 distribution