Introduction to Mathematical Statistics |
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Page 139
... result . 1 If , in Theorem 1 , we set each k¡ = 1 , we see that the sum of n mutually stochastically independent normally distributed variables has a normal distribution . The next theorem proves a similar result for chi - square ...
... result . 1 If , in Theorem 1 , we set each k¡ = 1 , we see that the sum of n mutually stochastically independent normally distributed variables has a normal distribution . The next theorem proves a similar result for chi - square ...
Page 247
... result shows that if we can find the p.d.f. of a sufficient statistic when the para- meter is assigned a special ... resulting statistic w [ u ( X1 , ... , Xn ) ] is called the maximum likelihood statistic for w ( 0 ) and it is denoted ...
... result shows that if we can find the p.d.f. of a sufficient statistic when the para- meter is assigned a special ... resulting statistic w [ u ( X1 , ... , Xn ) ] is called the maximum likelihood statistic for w ( 0 ) and it is denoted ...
Page 352
... result of part ( a ) to show that tr ( L'AL ) = tr A. ( c ) If A is a real symmetric idempotent matrix , use the result of part ( b ) to prove that the rank of A is equal to tr A. ji 13.9 . Let A = [ a1 ; ] be a real symmetric matrix ...
... result of part ( a ) to show that tr ( L'AL ) = tr A. ( c ) If A is a real symmetric idempotent matrix , use the result of part ( b ) to prove that the rank of A is equal to tr A. ji 13.9 . Let A = [ a1 ; ] be a real symmetric matrix ...
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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 F distribution function F(x given hypothesis H₁ 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 Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variables X₁ variance o² W₁ X₁ X₁ and X2 X₂ x²(n Y₂ Z₁ zero elsewhere μ₁ σ²