## Introduction to Mathematical Statistics |

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Page 4

This is indicated by

have the same elements, and this is indicated by

A1 = {r; 0 < r < 1} and A2 = {r; –1 = z < 2). Here the one-dimensional set A1 is

seen ...

This is indicated by

**writing**A 1 c A2. If A1 c A2 and also A2 c A1, the two setshave the same elements, and this is indicated by

**writing**A1 = A2. Example 1. LetA1 = {r; 0 < r < 1} and A2 = {r; –1 = z < 2). Here the one-dimensional set A1 is

seen ...

Page 13

If A is a subset of .2/, we would

the outcome of a random experiment is expressed as an ordered pair of numbers

, we can represent this outcome by the two random variables X and Y. Then ...

If A is a subset of .2/, we would

**write**P(A) = the probability that X e A = Pr(X e A). Ifthe outcome of a random experiment is expressed as an ordered pair of numbers

, we can represent this outcome by the two random variables X and Y. Then ...

Page 344

First we change the variables of integration in integral (2) from 21, a2, ..., a.m to yi

, y2, ..., ya by

suitable ordering of a1, a2, ..., an: We shall sometimes

anj.

First we change the variables of integration in integral (2) from 21, a2, ..., a.m to yi

, y2, ..., ya by

**writing**x – 1 = y, where y' = (y1, y2,..., y, The ... 0 0 . . . an for asuitable ordering of a1, a2, ..., an: We shall sometimes

**write**L'AL = diag|al, a2, ...,anj.

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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