## Introduction to mathematical statistics |

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Page 60

We shall next extend the

x2, . . ., xn\xi) is

xn\xj] is called the joint conditional p.d.f. of X2, . . . , Xn, given X1 = x1. The joint ...

We shall next extend the

**definition**of a conditional p.d.f. If fi(xi) > 0, the symbol f(x2, . . ., xn\xi) is

**defined**by the relation f\Xi, X2, . . . , Xn) f(x2, . =• A(*i) and f(x2, . . .,xn\xj] is called the joint conditional p.d.f. of X2, . . . , Xn, given X1 = x1. The joint ...

Page 258

a prescribed test, leads to the rejection of the hypothesis under consideration.

Then C is called the critical region of the test.

...

**Definition**3. Let C be that subset of the sample space which, in accordance witha prescribed test, leads to the rejection of the hypothesis under consideration.

Then C is called the critical region of the test.

**Definition**4. The power function of a...

Page 295

Unlike our previous likelihood ratio tests, the likelihood ratio does not

statistic which is a function of a statistic that has a well- known distribution (see

part (a), Exercise 11.10). Thus we cannot easily compute certain desirable ...

Unlike our previous likelihood ratio tests, the likelihood ratio does not

**define**astatistic which is a function of a statistic that has a well- known distribution (see

part (a), Exercise 11.10). Thus we cannot easily compute certain desirable ...

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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