## Introduction to Mathematical Statistics |

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Page 250

If we restrict our considerations to

where b does not depend upon y, show that R(0, w) = b” + 6/n. What

function of this form yields a uniformly smaller risk than every other

function ...

If we restrict our considerations to

**decision**functions of the form w(y) = b + y/n,where b does not depend upon y, show that R(0, w) = b” + 6/n. What

**decision**function of this form yields a uniformly smaller risk than every other

**decision**function ...

Page 260

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

incorrect

; accordingly, the significance level of the test is the probability of committing an ...

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

incorrect

**decision**or an error. This incorrect**decision**is often called a Type-I error; accordingly, the significance level of the test is the probability of committing an ...

Page 282

Lü's or, equivalently, if L(6') 2(9", 6")h(0") (2) IUF) Zū, Wilso If the sign of inequality

in expression (2) is reversed, we make the

members of expression (2) are equal, we can use some auxiliary random

experiment ...

Lü's or, equivalently, if L(6') 2(9", 6")h(0") (2) IUF) Zū, Wilso If the sign of inequality

in expression (2) is reversed, we make the

**decision**w = 6'; and if the twomembers of expression (2) are equal, we can use some auxiliary random

experiment ...

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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