## Introduction to Mathematical Statistics |

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Page 208

Why we use the terminology “

statistic Yi satisfies the preceding definition, then the conditional p.d.f. of Y2, say,

given Yi = yi, does not depend upon the parameter 6. As a consequence, once ...

Why we use the terminology “

**sufficient statistic**” can be explained as follows: If astatistic Yi satisfies the preceding definition, then the conditional p.d.f. of Y2, say,

given Yi = yi, does not depend upon the parameter 6. As a consequence, once ...

Page 218

sample from a distribution that has p.d. f. f(x; 6), 6 e Q, where it is known that Y1 =

u(X1, X2,..., Xn) is a

be another statistic (but not a function of Yi alone) which is an unbiased statistic ...

sample from a distribution that has p.d. f. f(x; 6), 6 e Q, where it is known that Y1 =

u(X1, X2,..., Xn) is a

**sufficient statistic**for the parameter 6, Let Y. – us(X, X2,..., X,)be another statistic (but not a function of Yi alone) which is an unbiased statistic ...

Page 233

That is, Z is stochastically independent of the

proved. If it is assumed that a statistic Z is stochastically independent of a statistic

Y1, then, of course, ga(z) = h(z) yi). It is interesting to observe that if Yi is a ...

That is, Z is stochastically independent of the

**sufficient statistic**Y1, as was to beproved. If it is assumed that a statistic Z is stochastically independent of a statistic

Y1, then, of course, ga(z) = h(z) yi). It is interesting to observe that if Yi is a ...

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### Common terms and phrases

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