Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 21
... probability set function must satisfy . Accordingly , P ( C2 | C1 ) is a probability set function , defined for subsets of C1 . It may be called the conditional probability set function , relative to the hypothesis C1 ; or the conditional ...
... probability set function must satisfy . Accordingly , P ( C2 | C1 ) is a probability set function , defined for subsets of C1 . It may be called the conditional probability set function , relative to the hypothesis C1 ; or the conditional ...
Page 23
... probability . From the definition of conditional probability , we have , using the law of total probability , that P ( C , | C ) = P ( CC ) P ( C ) = k P ( C ; ) P ( C | C ; ) Σ P ( C ) P ( CIC ) i = 1 which is the well - known Bayes ...
... probability . From the definition of conditional probability , we have , using the law of total probability , that P ( C , | C ) = P ( CC ) P ( C ) = k P ( C ; ) P ( C | C ; ) Σ P ( C ) P ( CIC ) i = 1 which is the well - known Bayes ...
Page 27
... conditional probability that there are at least three kings in the hand relative to the hypothesis that the hand contains at least two kings . 1.36 . A drawer contains eight pairs of socks ... Conditional Probability and Independence 27 27.
... conditional probability that there are at least three kings in the hand relative to the hypothesis that the hand contains at least two kings . 1.36 . A drawer contains eight pairs of socks ... Conditional Probability and Independence 27 27.
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A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²