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 158
... denote a random sample of size n from a given distribution . The statistic 1 X1 + X 2 + + Xn n X X = = n i = 1 n is called the mean of the random sample , and the ... random 158 Distributions of Functions of Random Variables [ Ch . 4.
... denote a random sample of size n from a given distribution . The statistic 1 X1 + X 2 + + Xn n X X = = n i = 1 n is called the mean of the random sample , and the ... random 158 Distributions of Functions of Random Variables [ Ch . 4.
Page 159
... denote a random sample . However , statisticians often use these symbols , X and S2 , even if the assumption of independence is dropped . For example , suppose that X1 , X2 , ... , X , were the observations taken at random from a finite ...
... denote a random sample . However , statisticians often use these symbols , X and S2 , even if the assumption of independence is dropped . For example , suppose that X1 , X2 , ... , X , were the observations taken at random from a finite ...
Page 162
... mean and the variance of the ratio Y = X1 / X2 . Hint : First find the distribution function Pr ( Y ≤ y ) when 0 < y < 1 and then when 1 ≤ y . 4.7 . Let X1 , X2 be a random sample from the distribution having p.d.f. f ( x ) = 2x , 0 ...
... mean and the variance of the ratio Y = X1 / X2 . Hint : First find the distribution function Pr ( Y ≤ y ) when 0 < y < 1 and then when 1 ≤ y . 4.7 . Let X1 , X2 be a random sample from the distribution having p.d.f. f ( x ) = 2x , 0 ...
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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