## Introduction to Mathematical Statistics |

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Page 221

Use this result to show that the family (b(2, 6); 0 < 0 < 1} is

infinite series ao + aiz + azz” + aaz” + . . . converges to zero for all values of z in a

given interval, then ao = a1 = az = aa = . . . = 0. Use this to prove that the family ...

Use this result to show that the family (b(2, 6); 0 < 0 < 1} is

**complete**. 8.17. If theinfinite series ao + aiz + azz” + aaz” + . . . converges to zero for all values of z in a

given interval, then ao = a1 = az = aa = . . . = 0. Use this to prove that the family ...

Page 222

E[p(Yi)] = 0 for all values of 6, 6 e Q. Let p(Yı) be another continuous function of

the sufficient statistic Yi alone so that we have also E[l (Yi)] = 0 for all values of 6,

6 e Q. Hence Esp(Yi) — p(Yi)] = 0, 6 e Q. If the family {g,(y1; 6); 6 e Q} is

, ...

E[p(Yi)] = 0 for all values of 6, 6 e Q. Let p(Yı) be another continuous function of

the sufficient statistic Yi alone so that we have also E[l (Yi)] = 0 for all values of 6,

6 e Q. Hence Esp(Yi) — p(Yi)] = 0, 6 e Q. If the family {g,(y1; 6); 6 e Q} is

**complete**, ...

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 depend upon 6 whether {g*(v1; 6); 6 e Q} is or is not

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 not

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