## Introduction to Mathematical Statistics |

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Page 40

This importance stems from the

unique and completely determines the distribution of the random variable; thus, if

two random variables have the same moment-generating function, they have the

...

This importance stems from the

**fact**that the moment-generating function isunique and completely determines the distribution of the random variable; thus, if

two random variables have the same moment-generating function, they have the

...

Page 106

As a matter of

and have positive standard deviations, we have noted in Example 4 of Section

2.4, p. 72, that p = 0. However, p = 0 does not in general imply that two variables

are ...

As a matter of

**fact**, if any two random variables are stochastically independentand have positive standard deviations, we have noted in Example 4 of Section

2.4, p. 72, that p = 0. However, p = 0 does not in general imply that two variables

are ...

Page 363

Since R has, when p = 0, a conditional distribution which does not depend upon

ri, a 2, ..., x, (and hence that conditional distribution is, in

distribution of R), we have the remarkable

independent of ...

Since R has, when p = 0, a conditional distribution which does not depend upon

ri, a 2, ..., x, (and hence that conditional distribution is, in

**fact**, the marginaldistribution of R), we have the remarkable

**fact**that R is stochasticallyindependent of ...

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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