Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 47
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 ...
Other editions - View all
Common terms and phrases
A₁ A₂ accept accordance Accordingly alternative approximately assume called cent Chapter complete compute Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given H₁ Hence hypothesis inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics parameter probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variables X1 variance W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁