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 221
... respectively . Given that the variance of Y = 3X2- X , is 25 , find k . o 4.106 . If the independent variables X , and X2 have means μ , μ2 and variances o , o , respectively , show that the mean and variance of the product Y = X1X2 are ...
... respectively . Given that the variance of Y = 3X2- X , is 25 , find k . o 4.106 . If the independent variables X , and X2 have means μ , μ2 and variances o , o , respectively , show that the mean and variance of the product Y = X1X2 are ...
Page 277
... respectively , independent random samples from the two distributions , N ( u ,, o2 ) and N ( μ2 , 02 ) , respectively . Denote the means of the samples by X and Ỹ and the variances of the samples by S and S2 , respectively . It should ...
... respectively , independent random samples from the two distributions , N ( u ,, o2 ) and N ( μ2 , 02 ) , respectively . Denote the means of the samples by X and Ỹ and the variances of the samples by S and S2 , respectively . It should ...
Page 297
... respectively , 13 , 19 , 11 , ( 1310 ) 2 10 - + ( 19 – 10 ) 2 ( 19 – 10 ) 2 + ( 11 ( 11-10 ) 2 ( 8-10 ) 2 + 10 10 10 - ( 5 — 10 ) 2 + + 10 ( 4-10 ) 2 10 = 15.6 Since 15.6 > 11.1 , the hypothesis P ( A ; ) = { , i = 1 , 2 , . . . , 6 ...
... respectively , 13 , 19 , 11 , ( 1310 ) 2 10 - + ( 19 – 10 ) 2 ( 19 – 10 ) 2 + ( 11 ( 11-10 ) 2 ( 8-10 ) 2 + 10 10 10 - ( 5 — 10 ) 2 + + 10 ( 4-10 ) 2 10 = 15.6 Since 15.6 > 11.1 , the hypothesis P ( A ; ) = { , i = 1 , 2 , . . . , 6 ...
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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.d.f. of Y₁ P(C₁ p₁ Poisson distribution positive integer probability density functions probability set function R₁ r₂ 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 Σ Σ σ²