Introduction to Mathematical Statistics |
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Page 94
... chi - square distribution ; and any f ( x ) of this form is called a chi - square p.d.f. The mean and the variance of a chi - square distribution are μ αβ aß = ( 1/2 ) 2 = r and o2 = α82 ( r / 2 ) 22 2r respectively . For no obvious ...
... chi - square distribution ; and any f ( x ) of this form is called a chi - square p.d.f. The mean and the variance of a chi - square distribution are μ αβ aß = ( 1/2 ) 2 = r and o2 = α82 ( r / 2 ) 22 2r respectively . For no obvious ...
Page 305
... chi - square distribution with ab 1 ( a + b − 2 ) = 1 ) ( b − 1 ) degrees of freedom , provided H。 is true . The hypothesis Ho is then rejected if the computed value of this statistic exceeds the constant c , where c is selected from ...
... chi - square distribution with ab 1 ( a + b − 2 ) = 1 ) ( b − 1 ) degrees of freedom , provided H。 is true . The hypothesis Ho is then rejected if the computed value of this statistic exceeds the constant c , where c is selected from ...
Page 312
... square distribution with a ( b − 1 ) degrees of freedom . Now a Σ . - Q2 = 6 1⁄2 ( Ã ̧ . – X ) 2 ≥ 0. In accordance with the theorem , Q1 and Q2 are i = 1 - stochastically independent , and Q2 / 02 has a chi - square distribution with ...
... square distribution with a ( b − 1 ) degrees of freedom . Now a Σ . - Q2 = 6 1⁄2 ( Ã ̧ . – X ) 2 ≥ 0. In accordance with the theorem , Q1 and Q2 are i = 1 - stochastically independent , and Q2 / 02 has a chi - square distribution with ...
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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