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Page 59
... joint p.d.f. f ( x1 , x2 , x2 , ... , xn ) . If the random variables are of the continuous type , then by an argument similar to the two - variable case , we have for every a < b , Pr ( a < X1 < b ) = √ ° ƒ1 ( x1 ) dx1 , 1 ( x1 ) where ...
... joint p.d.f. f ( x1 , x2 , x2 , ... , xn ) . If the random variables are of the continuous type , then by an argument similar to the two - variable case , we have for every a < b , Pr ( a < X1 < b ) = √ ° ƒ1 ( x1 ) dx1 , 1 ( x1 ) where ...
Page 60
... joint conditional p.d.f. of any n 1 random variables , say , X1 , ... , X1 - 1 , Xi + 1 , ... , Xn , given X1 = x , is defined as the joint p.d.f. of X1 , X2 , ... , X2 divided by marginal p.d.f. ƒ¡ ( x¡ ) , provided f ( x ) > 0. More ...
... joint conditional p.d.f. of any n 1 random variables , say , X1 , ... , X1 - 1 , Xi + 1 , ... , Xn , given X1 = x , is defined as the joint p.d.f. of X1 , X2 , ... , X2 divided by marginal p.d.f. ƒ¡ ( x¡ ) , provided f ( x ) > 0. More ...
Page 115
... p.d.f. of Y1 is given by V1 81 ( 91 ) = Σg ( Y1 , Y2 ) V2 = 0 e - 41-42 31 = y1 ! V2 = 0 ( 31 - = = y1 ! - Y2 ) ! Y2 ... joint p.d.f. of X1 and X2 , find the joint p.d.f. of Y1 = X1 = X2 and Y2 = X1 + X2 . 1 - 2 4.14 . Let X have the ...
... p.d.f. of Y1 is given by V1 81 ( 91 ) = Σg ( Y1 , Y2 ) V2 = 0 e - 41-42 31 = y1 ! V2 = 0 ( 31 - = = y1 ! - Y2 ) ! Y2 ... joint p.d.f. of X1 and X2 , find the joint p.d.f. of Y1 = X1 = X2 and Y2 = X1 + X2 . 1 - 2 4.14 . Let X have the ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider 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 H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions 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 theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ