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Page 84
... Hence the conditional mean of Y , given X = x , is the linear function E ( Y❘x ) = ( n - x ) P2 1- Pi Likewise , we find that the conditional distribution of X , given Y = y , is b [ n - y , P1 / ( 1 P2 ) ] and thus E ( Xly ) = ( n - y ) ...
... Hence the conditional mean of Y , given X = x , is the linear function E ( Y❘x ) = ( n - x ) P2 1- Pi Likewise , we find that the conditional distribution of X , given Y = y , is b [ n - y , P1 / ( 1 P2 ) ] and thus E ( Xly ) = ( n - y ) ...
Page 101
... Hence the p.d.f. g ( v ) = G ' ( v ) of the continuous - type random variable V is 1 g ( v ) = v1 / 2-1e - v / 2 , 0 < v < ∞ , V & V 2 = 0 elsewhere . Since g ( v ) is a p.d.f. and hence it must be that г ( 1 ) EXERCISES 3.34 . If So 8 ...
... Hence the p.d.f. g ( v ) = G ' ( v ) of the continuous - type random variable V is 1 g ( v ) = v1 / 2-1e - v / 2 , 0 < v < ∞ , V & V 2 = 0 elsewhere . Since g ( v ) is a p.d.f. and hence it must be that г ( 1 ) EXERCISES 3.34 . If So 8 ...
Page 123
... hence the joint p.d.f. of Y1 and Y2 is g ( Y1 , y2 ) 1 = || 1121 e - 11-12 , ( Y1 , Y2 ) = B , = 0 elsewhere . Thus the p.d.f. of Y1 is given by or 1 8 ( 91 ) = [ _an - 201 1 2 1 e - 1-2 dy2 = 1 ,, < y < 0 , 1 = e - 41-42 dy2 2 = le ...
... hence the joint p.d.f. of Y1 and Y2 is g ( Y1 , y2 ) 1 = || 1121 e - 11-12 , ( Y1 , Y2 ) = B , = 0 elsewhere . Thus the p.d.f. of Y1 is given by or 1 8 ( 91 ) = [ _an - 201 1 2 1 e - 1-2 dy2 = 1 ,, < y < 0 , 1 = e - 41-42 dy2 2 = le ...
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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