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 85
... given X1 = x1 , which can be written more simply as var ( X2 | x1 ) . It is convenient to refer to these as the " conditional mean " and the " conditional variance " of X2 , given X1 = x1 . Of course , we have - var ( X2 | x1 ) = E ( X } ...
... given X1 = x1 , which can be written more simply as var ( X2 | x1 ) . It is convenient to refer to these as the " conditional mean " and the " conditional variance " of X2 , given X1 = x1 . Of course , we have - var ( X2 | x1 ) = E ( X } ...
Page 110
... given X1 = x1 . The joint conditional p.d.f. of any n − 1 random variables , say X1 , ... , Xi - 1 , Xi + 1 , ... , Xn , given X1 = x1 , is defined as the joint p.d.f. of X1 , X2 , ... , X , divided by the marginal p.d.f. f ( x ) ...
... given X1 = x1 . The joint conditional p.d.f. of any n − 1 random variables , say X1 , ... , Xi - 1 , Xi + 1 , ... , Xn , given X1 = x1 , is defined as the joint p.d.f. of X1 , X2 , ... , X , divided by the marginal p.d.f. f ( x ) ...
Page 148
... given that X = x . That is , the conditional p.d.f. of Y , given X = x , is itself normal with mean μ2 + p ( σ2 / σ1 ) ( x - μ1 ) and variance o2 ( 1 − p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y ...
... given that X = x . That is , the conditional p.d.f. of Y , given X = x , is itself normal with mean μ2 + p ( σ2 / σ1 ) ( x - μ1 ) and variance o2 ( 1 − p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y ...
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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 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