## Introduction to mathematical statistics |

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Page 139

The next theorem proves a similar

X1, X2, . . . , Xn be mutually stochastically independent variables that have,

respectively, the chi-square distributions x2(ri), X2(r2), . . ., an^x2(rn)- Then the ...

The next theorem proves a similar

**result**for chi-square variables. Theorem 2. LetX1, X2, . . . , Xn be mutually stochastically independent variables that have,

respectively, the chi-square distributions x2(ri), X2(r2), . . ., an^x2(rn)- Then the ...

Page 247

It g(y; 80) is the p.d.f. of the sufficient statistic Y in the special case 8 = 90, then the

p.d.f. g(y; 8) of the sufficient statistic Y for every 8 e D. is given by g(y; 9) = g(y; e0)

This

It g(y; 80) is the p.d.f. of the sufficient statistic Y in the special case 8 = 90, then the

p.d.f. g(y; 8) of the sufficient statistic Y for every 8 e D. is given by g(y; 9) = g(y; e0)

This

**result**proves useful in certain difficult distribution problems. The**result**...Page 352

(b) If A is a square matrix and if L is an orthogonal matrix, use the

to show that tr (L'AL) = tr A. (c) If A is a real symmetric idempotent matrix, use the

(b) If A is a square matrix and if L is an orthogonal matrix, use the

**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. 13.9. Let A = [atj] be a ...### What people are saying - Write a review

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Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere