## Introduction to mathematical statistics |

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Page 260

The rejection of the hypothesis H0 when that hypothesis is true is, of course, an

incorrect decision or an error. ... To test the

alternative simple hypothesis H1:8 = 2 use a random sample X1,X2 of size n = 2

...

The rejection of the hypothesis H0 when that hypothesis is true is, of course, an

incorrect decision or an error. ... To test the

**simple hypothesis H0**: 8=\ against thealternative simple hypothesis H1:8 = 2 use a random sample X1,X2 of size n = 2

...

Page 268

n C = {(»j,..., xn); 2*1 ^ c) is a best critical region for testing H0: p = % i against H1

: p = J. Use the central limit theorem to ... 10.3 Uniformly Most Powerful Tests This

section will take up the problem of a test of a

n C = {(»j,..., xn); 2*1 ^ c) is a best critical region for testing H0: p = % i against H1

: p = J. Use the central limit theorem to ... 10.3 Uniformly Most Powerful Tests This

section will take up the problem of a test of a

**simple hypothesis H0**against an ...Page 273

10.26. Let X1, X2, . . . , Xn be a random sample of size n from a distribution which

has p.d.f. f(x; 91, 82) = 82e~e2(x~ei\ 91 < x < oo, zero elsewhere. Find a best

critical region for testing the

the ...

10.26. Let X1, X2, . . . , Xn be a random sample of size n from a distribution which

has p.d.f. f(x; 91, 82) = 82e~e2(x~ei\ 91 < x < oo, zero elsewhere. Find a best

critical region for testing the

**simple hypothesis H0**: 91 = 9[, 82 = 8'2 > 0, againstthe ...

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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