## Introduction to Mathematical Statistics |

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Page 59

All of the preceding definitions can be directly generalized to the case of n

variables in the following manner. Let the random variables X1, X2,..., Xn have

the

, then ...

All of the preceding definitions can be directly generalized to the case of n

variables in the following manner. Let the random variables X1, X2,..., Xn have

the

**joint p.d. f.**f(x1, x2, ..., a.m.). If the random variables are of the continuous type, then ...

Page 60

We shall next extend the definition of a conditional

, ..., xn|a'i) is defined by the relation f(x1, 22, . . . , *..), f(x2, ..., walr1) = fi (r.1) and f(

x2, ..., zn|z1) is called the

We shall next extend the definition of a conditional

**p.d.f.**If f(z) > 0, the symbol f(x2, ..., xn|a'i) is defined by the relation f(x1, 22, . . . , *..), f(x2, ..., walr1) = fi (r.1) and f(

x2, ..., zn|z1) is called the

**joint**conditional**p.d.f.**of X2,..., Xn, given X1 = 21.Page 114

From this

on ya or the marginal p.d.f. of Y2 by Summing on y1. Perhaps it should be

emphasized that the technique of change of variables involves the introduction of

as ...

From this

**joint p.d. f.**g(y1, y2) we may obtain the marginal p.d.f. of Yi by summingon ya or the marginal p.d.f. of Y2 by Summing on y1. Perhaps it should be

emphasized that the technique of change of variables involves the introduction of

as ...

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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