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 100
... p.d.f. of X and Y. Show that the conditional means are , respectively , ( 1 + x ) / 2 , 0 < x < 1 , and y / 2 , 0 ... y < x , 0 < x < 1 , zero elsewhere . Show that , on the set of positive probability density , the graph of E ( Yx ) is ...
... p.d.f. of X and Y. Show that the conditional means are , respectively , ( 1 + x ) / 2 , 0 < x < 1 , and y / 2 , 0 ... y < x , 0 < x < 1 , zero elsewhere . Show that , on the set of positive probability density , the graph of E ( Yx ) is ...
Page 162
... p.d.f. f ( x ) = 4x3 , 0 < x < 1 , zero elsewhere . Show that Y = 2 ln X is ... Y X } + X2 . = Hint : In the double integral representing Pr ( Y≤ y ) , use ... Y = X + X2 . Find the distribution function and the p.d.f. of Y. 4.14 . Let ...
... p.d.f. f ( x ) = 4x3 , 0 < x < 1 , zero elsewhere . Show that Y = 2 ln X is ... Y X } + X2 . = Hint : In the double integral representing Pr ( Y≤ y ) , use ... Y = X + X2 . Find the distribution function and the p.d.f. of Y. 4.14 . Let ...
Page 212
... p.d.f. , and that these n pairs are independent . The twofold integral in ... Y = X + X2 . Note , under appropriate assumptions , that Y may be interpreted as the ... Y X X2 + n2 has a binomial distribution with parameters n = n1 + n2 , p ...
... p.d.f. , and that these n pairs are independent . The twofold integral in ... Y = X + X2 . Note , under appropriate assumptions , that Y may be interpreted as the ... Y X X2 + n2 has a binomial distribution with parameters n = n1 + n2 , p ...
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Common terms and phrases
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. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. 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 X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²