Introduction to the Theory of Statistics
McGraw-Hill, 1973 - Mathematics - 564 pages
Probability; Random variables, distribution functions, and expectation; Special parametric families of univariate distributions; Joint and conditional distributions, stochastic independence, more expectation; Distributions of functions of random variables; Sampling and sampling distributions; Parametric interval estimation; Tests of hypotheses; Linear models; Nonparametric method.
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approximately assume balls binomial called Chap chapter coin collection conditional confidence interval consists contains corresponding cumulative distribution function defined Definition degrees of freedom denote depend derived determine discrete discussed drawn equal error event EXAMPLE exists expected experiment Find fixed fx(x given gives head hence hypothesis independent indicated integer joint jointly known Let X1 limiting maximum-likelihood estimator mean measure method moment moments normal distribution Note observations obtained outcomes P[AB parameter particular percent population positive possible powerful probability probability density function problem PROOF properties Prove random sample random variable Reject Remark replacement respect result sample mean sample space satisfying selected simple statistics subsets sufficient statistics Suppose Theorem theory tion tossing trial true unbiased estimator uniformly values variance