## Introduction to mathematical statistics |

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Page 179

These random variables are mutually stochastically independent and each, in

F(X1), F(X2), .... F(Xn) is a random sample of size n from a uniform distribution on

...

These random variables are mutually stochastically independent and each, in

**accordance**with Theorem 1, has a uniform distribution on the interval (0, 1). ThusF(X1), F(X2), .... F(Xn) is a random sample of size n from a uniform distribution on

...

Page 258

Robert V. Hogg, Allen Thornton Craig. Definition 3. Let C be that subset of the

sample space which, in

of the hypothesis under consideration. Then C is called the critical region of the

test.

Robert V. Hogg, Allen Thornton Craig. Definition 3. Let C be that subset of the

sample space which, in

**accordance**with a prescribed test, leads to the rejectionof the hypothesis under consideration. Then C is called the critical region of the

test.

Page 279

We wish to test the simple hypothesis H0: 8 = 8' against the simple hypothesis H1

: 8 = 8". Thus the parameter space is Q = [8; 8 = 8', 8"}. In

decision function procedure, we need a function w of the observed values ot X1,

...

We wish to test the simple hypothesis H0: 8 = 8' against the simple hypothesis H1

: 8 = 8". Thus the parameter space is Q = [8; 8 = 8', 8"}. In

**accordance**with thedecision function procedure, we need a function w of the observed values ot X1,

...

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### Common terms and phrases

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