## Introduction to Mathematical Statistics |

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Page 228

n(n − 1)[max (r) — min (c)]"-" Since the last factor does not

parameters, the FisherNeyman criterion assures us that Yi and Yn are joint

sufficient statistics for 6, and 62. This result can also be established by showing

that the ...

n(n − 1)[max (r) — min (c)]"-" Since the last factor does not

**depend**upon theparameters, the FisherNeyman criterion assures us that Yi and Yn are joint

sufficient statistics for 6, and 62. This result can also be established by showing

that the ...

Page 232

Let Z = u(X1, X2,..., Xn) be any other statistic (not a function of Yı alone). If the

distribution of Z does not

the sufficient statistic Y1. Proof. We shall prove a special case of this theorem.

Let Z = u(X1, X2,..., Xn) be any other statistic (not a function of Yı alone). If the

distribution of Z does not

**depend**upon 0, then Z is stochastically independent ofthe sufficient statistic Y1. Proof. We shall prove a special case of this theorem.

Page 233

It is interesting to observe that if Yi is a sufficient statistic for 6, then h(z) yi), and

hence ga(z), does not

complete. That is, the theorem may not be stated as an “if, and only if,” condition

for the ...

It is interesting to observe that if Yi is a sufficient statistic for 6, then h(z) yi), and

hence ga(z), does not

**depend**upon 6 whether {g*(v1; 6); 6 e Q} is or is notcomplete. That is, the theorem may not be stated as an “if, and only if,” condition

for the ...

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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