## Introduction to Mathematical Statistics |

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Page 256

I rejecting the hypothesis Ho: 0 < 75 is 4. That is, if 0 = 75 so that Ho is

probability of rejecting this

research workers find it very undesirable to have such a high probability as 4

assigned to ...

I rejecting the hypothesis Ho: 0 < 75 is 4. That is, if 0 = 75 so that Ho is

**true**, theprobability of rejecting this

**true**hypothesis Ho is 4. Many statisticians andresearch workers find it very undesirable to have such a high probability as 4

assigned to ...

Page 259

i. e-Gri + ra)12 dri data O 0. 4. = 0.05 approximately. If H 1 is

the joint p.d.f. of X1 and X2 is f(r1; 4)f(x2; 4) = H'ge-“I “a”, 0 < a. i < OO, 0 < x2 < 00

, = 0 elsewhere, and 9.5-ra 1 9.5 Pr[(X1, X2) e C] = 1 – ...

i. e-Gri + ra)12 dri data O 0. 4. = 0.05 approximately. If H 1 is

**true**, that is, 0 = 4,the joint p.d.f. of X1 and X2 is f(r1; 4)f(x2; 4) = H'ge-“I “a”, 0 < a. i < OO, 0 < x2 < 00

, = 0 elsewhere, and 9.5-ra 1 9.5 Pr[(X1, X2) e C] = 1 – ...

Page 325

Qs/o” are stochastically independent and chi-square (possibly noncentral), even

though the mean of Xu is u + ot. We shall compute the noncentrality parameters

of Qa/a" and Qs/o" when Ho is

...

Qs/o” are stochastically independent and chi-square (possibly noncentral), even

though the mean of Xu is u + ot. We shall compute the noncentrality parameters

of Qa/a" and Qs/o" when Ho is

**true**. We have E(X) = u + at E(X) = u + xi, E(X) = p,...

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accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere