## 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

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

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

, then ...

Page 68

and 6°/(0, 0) yield the means, the variances, and the covariance of the two

means, variances, and correlation coefficients denoted by p.1, u2, pla; of, of, oo;

and pia, ...

and 6°/(0, 0) yield the means, the variances, and the covariance of the two

**random variables**. T 2.24. Let**X1**, X2, and Xa be three**random variables**withmeans, variances, and correlation coefficients denoted by p.1, u2, pla; of, of, oo;

and pia, ...

Page 74

With random variables of the discrete type, the proof is made by using summation

instead of integration. Let the

(x1, x2, ..., xm) and the marginal probability density functions fi(x1), f2(z2), ..., f ...

With random variables of the discrete type, the proof is made by using summation

instead of integration. Let the

**random variables X1**, X2,..., Xn have the joint p.d.f. f(x1, x2, ..., xm) and the marginal probability density functions fi(x1), f2(z2), ..., f ...

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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