Introduction to Mathematical Statistics |
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Page 57
... given that the continuous type of random variable X1 has the value x1 . When ƒ2 ( x2 ) > 0 , the conditional p.d.f. of the continuous type of random variable X1 , given that the con- tinuous type of random variable X2 has the value x2 ...
... given that the continuous type of random variable X1 has the value x1 . When ƒ2 ( x2 ) > 0 , the conditional p.d.f. of the continuous type of random variable X1 , given that the con- tinuous type of random variable X2 has the value x2 ...
Page 60
... given X1 = x1 . The 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 ...
... given X1 = x1 . The 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 ...
Page 104
... given X = o2 ( 1 - - x , is itself normal with mean μ2 + p ( 02/01 ) ( x − μ1 ) and variance p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y , given X = x , is linear in x and is given by 02 E ( Y❘x ) ...
... given X = o2 ( 1 - - x , is itself normal with mean μ2 + p ( 02/01 ) ( x − μ1 ) and variance p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y , given X = x , is linear in x and is given by 02 E ( Y❘x ) ...
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Common terms and phrases
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