## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 86

Page 205

In this connection, we need the following

whose mathematical expectation is equal to a parameter 6 is called an unbiased

statistic for the parameter 6. Otherwise the statistic is said to be biased. Now it ...

In this connection, we need the following

**definition**.**Definition**1. Any statisticwhose mathematical expectation is equal to a parameter 6 is called an unbiased

statistic for the parameter 6. Otherwise the statistic is said to be biased. Now it ...

Page 258

a prescribed test, leads to the rejection of the hypothesis under consideration.

Then C is called the critical region of the test.

...

**Definition**3. Let C be that subset of the sample space which, in accordance witha prescribed test, leads to the rejection of the hypothesis under consideration.

Then C is called the critical region of the test.

**Definition**4. The power function of a...

Page 261

Under this restriction, we shall do three things: (a)

against H1. - (b) Prove a theorem which provides a method of determining a best

test. (c) Give two examples. Before we

Under this restriction, we shall do three things: (a)

**Define**a best test for testing Hoagainst H1. - (b) Prove a theorem which provides a method of determining a best

test. (c) Give two examples. Before we

**define**a best test, one important ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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