Introduction to Mathematical Statistics |
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Page 75
... independence of X1 , X2 , . . . , Xn · 3 Remark . If X1 , X2 , and X ̧ are mutually stochastically independent , they are pairwise stochastically independent ( that is , X , and X ,, i j , where i , j = 1 , 2 , 3 are stochastically ...
... independence of X1 , X2 , . . . , Xn · 3 Remark . If X1 , X2 , and X ̧ are mutually stochastically independent , they are pairwise stochastically independent ( that is , X , and X ,, i j , where i , j = 1 , 2 , 3 are stochastically ...
Page 77
... stochastically independent and that E ( et ( x1 + x2 ) ) = ( 1 − t ) -2 , t < 1 . = 1 2.31 . Let X1 , X2 , X ̧ , and X be four mutually stochastically inde- pendent random variables , each with p.d.f. f ( x ) 3 ( 1x ) 2 , 0 < x < 1 ...
... stochastically independent and that E ( et ( x1 + x2 ) ) = ( 1 − t ) -2 , t < 1 . = 1 2.31 . Let X1 , X2 , X ̧ , and X be four mutually stochastically inde- pendent random variables , each with p.d.f. f ( x ) 3 ( 1x ) 2 , 0 < x < 1 ...
Page 134
... mutually stochastically independent . and ẞ = 1 , i = 1 , 2 , ... , r , ß : 4.37 . Let X1 , X2 , ... , X , be r mutually stochastically independent gamma variables with parameters a = a , respectively . Show that Y1 = X1 + X2 + ··· tion ...
... mutually stochastically independent . and ẞ = 1 , i = 1 , 2 , ... , r , ß : 4.37 . Let X1 , X2 , ... , X , be r mutually stochastically independent gamma variables with parameters a = a , respectively . Show that Y1 = X1 + X2 + ··· tion ...
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A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²