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 12
... subset of % , then P ( C ) is the probability that the outcome of the random experiment is an element of C. Henceforth it will be tacitly assumed that the structure of each set C is sufficiently simple to allow the computation . We have ...
... subset of % , then P ( C ) is the probability that the outcome of the random experiment is an element of C. Henceforth it will be tacitly assumed that the structure of each set C is sufficiently simple to allow the computation . We have ...
Page 29
... subset of A , let C be that subset of such that C = { c : ce % and X ( c ) e A } . Thus C has as its elements all outcomes in 6 for which the random variable X has a value that is in A. This prompts us to define , as we now do , Pr ( Xe ...
... subset of A , let C be that subset of such that C = { c : ce % and X ( c ) e A } . Thus C has as its elements all outcomes in 6 for which the random variable X has a value that is in A. This prompts us to define , as we now do , Pr ( Xe ...
Page 30
... subset of , and P ( C ) means the probability of C , a subset of % . From this point on , we shall adopt this convention and simply write P ( A ) . = = Perhaps an additional example will be helpful . Let a coin be tossed two independent ...
... subset of , and P ( C ) means the probability of C , a subset of % . From this point on , we shall adopt this convention and simply write P ( A ) . = = Perhaps an additional example will be helpful . Let a coin be tossed two independent ...
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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 Find the p.d.f. g₁(y₁ gamma distribution given Hint hypothesis H₁ independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics 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 subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ Σ Σ σ²