Introduction to Probability Theory and Statistical Inference
Discusses probability theory and to many methods used in problems of statistical inference. The Third Edition features material on descriptive statistics. Cramer-Rao bounds for variance of estimators, two-sample inference procedures, bivariate normal probability law, F-Distribution, and the analysis of variance and non-parametric procedures. Contains numerous practical examples and exercises.
Random Variables and Distribution Functions
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approximately Assume average balls binomial bulbs called coin compute confidence interval consists constant contains continuous defective defined DEFINITION degrees of freedom density function derive discrete discussed distribution function elements equal equations error estimator evaluate exactly EXAMPLE Exercise expected experiment exponential fact Figure flip Fx(t given gives H₁ hypothesis independent integer interval known least length maximum likelihood estimator mean measure method moments normal random variable normally distributed Note observed observed value occur otherwise outcomes particular population positive possible posterior prior probability function problem Proof Px(x random sample range reasonable region reject respectively result sample space selected Show simple specified squares standard statistic student subsets Suppose Table Theorem trials true variable with parameter variance versus weight zero