## Introduction to Mathematical Statistics |

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Page 33

spade. Then E: is the set of outcomes in which no card is a spade. There are r = (.

..) such outcomes. Hence (...) P(E)=\; and P(E) = 1 - P(E) (...) 5 Now suppose Ea ...

**approximately**. Next, let E2 be the set of outcomes in which at least one card is aspade. Then E: is the set of outcomes in which no card is a spade. There are r = (.

..) such outcomes. Hence (...) P(E)=\; and P(E) = 1 - P(E) (...) 5 Now suppose Ea ...

Page 259

i. e-Gri + ra)12 dri data O 0. 4. = 0.05

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 281

If we use Table III of the Appendix, we see, by trial and error, that the solution is c

= 76.8,

If we use Table III of the Appendix, we see, by trial and error, that the solution is c

= 76.8,

**approximately**. The significance level of the test is 1 – N(1.8) = 0.036,**approximately**, and the power of the test when Hi is true is 1 – N(–1.2) = 0.885, ...### What people are saying - Write a review

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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