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 111
... Xn ) . As in the cases of one and two variables , this m.g.f. is unique and uniquely determines the joint distribution of the n n variables ( and hence all marginal distributions ) . For Sec . 2.5 ] Extension to Several Random Variables ...
... Xn ) . As in the cases of one and two variables , this m.g.f. is unique and uniquely determines the joint distribution of the n n variables ( and hence all marginal distributions ) . For Sec . 2.5 ] Extension to Several Random Variables ...
Page 114
... independent random variables , each with p.d.f. f ( x ) = 3 ( 1 − x ) 2 , 0 < x < 1 , zero elsewhere . If Y is the minimum of these four variables , find the distribution function and the p.d.f. of Y. 2.40 . A fair die is cast at ...
... independent random variables , each with p.d.f. f ( x ) = 3 ( 1 − x ) 2 , 0 < x < 1 , zero elsewhere . If Y is the minimum of these four variables , find the distribution function and the p.d.f. of Y. 2.40 . A fair die is cast at ...
Page 221
... two independent random variables so that the variances of X , and X2 are σ = k and σ = 2 , respectively . Given that the variance of Y = 3X2 - X , is 25 , find k . 4.106 . If the independent variables X , and X2 have means μ1 , μ2 and ...
... two independent random variables so that the variances of X , and X2 are σ = k and σ = 2 , respectively . Given that the variance of Y = 3X2 - X , is 25 , find k . 4.106 . If the independent variables X , and X2 have means μ1 , μ2 and ...
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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