Introduction to Mathematical Statistics |
From inside the book
Results 1-3 of 86
Page 69
... ( x1 ) f2 ( x2 ) means a function that is positive on a product space . That is , if ƒ1 ( x1 ) and ƒ1⁄2 ( x2 ) are positive on , and only on , the ... X1 and X2 are stochastically independent , Sect . 2.4 ] Stochastic Independence 69.
... ( x1 ) f2 ( x2 ) means a function that is positive on a product space . That is , if ƒ1 ( x1 ) and ƒ1⁄2 ( x2 ) are positive on , and only on , the ... X1 and X2 are stochastically independent , Sect . 2.4 ] Stochastic Independence 69.
Page 70
... ( x1 , x2 ) = f1 ( x1 ) f2 ( x2 ) , where ƒ1 ( x1 ) and ƒ2 ( x2 ) are the marginal probability density functions of X1 and X2 respectively . Thus , the condition f ( x1 , xX2 ) = g ( x1 ) h ( x2 ) is fulfilled . Conversely , if f ( x1 ...
... ( x1 , x2 ) = f1 ( x1 ) f2 ( x2 ) , where ƒ1 ( x1 ) and ƒ2 ( x2 ) are the marginal probability density functions of X1 and X2 respectively . Thus , the condition f ( x1 , xX2 ) = g ( x1 ) h ( x2 ) is fulfilled . Conversely , if f ( x1 ...
Page 72
... X1 and X2 have the marginal probability density functions f1 ( x1 ) and f2 ( x2 ) respectively . The expected value of the product of a function u ( X1 ) of X1 alone and a function v ( X2 ) of X2 alone is , subject to their existence ...
... X1 and X2 have the marginal probability density functions f1 ( x1 ) and f2 ( x2 ) respectively . The expected value of the product of a function u ( X1 ) of X1 alone and a function v ( X2 ) of X2 alone is , subject to their existence ...
Other editions - View all
Common terms and phrases
A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval 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 hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function 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 t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²