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Page 59
... marginal and conditional probability density functions from the point of ... p.d.f. f ( x1 , x2 , x2 , ... , xn ) . If the random variables are of the ... p.d.f. of the one random variable X1 and f ( x ) is called the marginal p.d.f. of ...
... marginal and conditional probability density functions from the point of ... p.d.f. f ( x1 , x2 , x2 , ... , xn ) . If the random variables are of the ... p.d.f. of the one random variable X1 and f ( x ) is called the marginal p.d.f. of ...
Page 60
... 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 generally , the ...
... 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 generally , the ...
Page 114
... p.d.f. g ( y1 , Y2 ) we may obtain the marginal p.d.f. of Y1 by summing on y2 or the marginal p.d.f. of Y2 by summing on y1 . 1 Perhaps it should be emphasized that the technique of change of variables involves the introduction of as ...
... p.d.f. g ( y1 , Y2 ) we may obtain the marginal p.d.f. of Y1 by summing on y2 or the marginal p.d.f. of Y2 by summing on y1 . 1 Perhaps it should be emphasized that the technique of change of variables involves the introduction of as ...
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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