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 110
... joint p.d.f. of the n random variables X1 , X2 , ... , X , just as before . Now , however , let us take any group of k < n of these random variables and let us find the joint p.d.f. of them . This joint p.d.f. is called the marginal p.d.f. ...
... joint p.d.f. of the n random variables X1 , X2 , ... , X , just as before . Now , however , let us take any group of k < n of these random variables and let us find the joint p.d.f. of them . This joint p.d.f. is called the marginal p.d.f. ...
Page 167
... joint p.d.f. of X , and X2 , find the joint p.d.f. of Y1 = X1 - X2 and Y2 = X1 + X2 . 4.19 . Let X have the p.d.f. f ( x ) = ( } ) ' , x = 1 , 2 , 3 , . . . , zero elsewhere . Find the p.d.f. of Y = X3 . 4.20 . Let X and X2 have the joint ...
... joint p.d.f. of X , and X2 , find the joint p.d.f. of Y1 = X1 - X2 and Y2 = X1 + X2 . 4.19 . Let X have the p.d.f. f ( x ) = ( } ) ' , x = 1 , 2 , 3 , . . . , zero elsewhere . Find the p.d.f. of Y = X3 . 4.20 . Let X and X2 have the joint ...
Page 202
... p.d.f. f ( x ) = 2 ( 1 − x ) , 0 < x < 1 , zero elsewhere , compute the probability that one sample observation is ... joint p.d.f. of Y , and Y2 , and first integrating on y1 . ( b ) Find the covariance of Y , and Y2 . 4.67 . Let Y ...
... p.d.f. f ( x ) = 2 ( 1 − x ) , 0 < x < 1 , zero elsewhere , compute the probability that one sample observation is ... joint p.d.f. of Y , and Y2 , and first integrating on y1 . ( b ) Find the covariance of Y , and Y2 . 4.67 . Let 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 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