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 251
... approximate normal distributions . For illustration , Y , of Example 2 has an approximate No [ np , np ( 1 − p ) ] . So np ( 1 − p ) is an important function of p as it is the variance of Y. Thus , if p is unknown , we might want to ...
... approximate normal distributions . For illustration , Y , of Example 2 has an approximate No [ np , np ( 1 − p ) ] . So np ( 1 − p ) is an important function of p as it is the variance of Y. Thus , if p is unknown , we might want to ...
Page 252
... approximate normal distribution with mean arcsin √p and variance 1 / 4n , which is free of p . EXERCISES 5.20 . Let X denote the mean of a random sample of size 100 from a distri- bution that is x2 ( 50 ) . Compute an approximate value ...
... approximate normal distribution with mean arcsin √p and variance 1 / 4n , which is free of p . EXERCISES 5.20 . Let X denote the mean of a random sample of size 100 from a distri- bution that is x2 ( 50 ) . Compute an approximate value ...
Page 273
... approximate is due to the fact that Y has a distribution of the discrete type and thus it is , in general , impossible to achieve the probability 0.95 exactly . With c1 ( p ) and c2 ( p ) increasing functions , they have single - valued ...
... approximate is due to the fact that Y has a distribution of the discrete type and thus it is , in general , impossible to achieve the probability 0.95 exactly . With c1 ( p ) and c2 ( p ) increasing functions , they have single - valued ...
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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