## Introduction to Mathematical Statistics |

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Page 220

Let u(x) denote a continuous function of a (but not a function of 6). If E[u(X)] = 0 for

every 6, 6 e Q, requires u(x) to be zero at each point at at which at least one

member of the family of

...

Let u(x) denote a continuous function of a (but not a function of 6). If E[u(X)] = 0 for

every 6, 6 e Q, requires u(x) to be zero at each point at at which at least one

member of the family of

**probability density functions**is positive, then the family of...

Page 223

Find the unique continuous function of this statistic that is the best statistic for 6.

8.7 The Exponential Class of

6); 6 e Q} of

Find the unique continuous function of this statistic that is the best statistic for 6.

8.7 The Exponential Class of

**Probability Density Functions**Consider a family {f(x;6); 6 e Q} of

**probability density functions**, where Q is the interval set Q = {0; y < 0 ...Page 228

Accordingly the joint p.d.f. of X1, X2,..., Xn can be written, for points of positive

probability density, ( 1 ) - n(n − 1)[max (c) ... However, the concept of a complete

family of

...

Accordingly the joint p.d.f. of X1, X2,..., Xn can be written, for points of positive

probability density, ( 1 ) - n(n − 1)[max (c) ... However, the concept of a complete

family of

**probability density functions**is generalized as follows: Let {f(t1, W2, ..., v.;...

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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