## Introduction to Mathematical Statistics |

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Page 108

It should be noted that, although a statistic does not depend upon any

parameter, the distribution of that statistic may very well depend upon

parameters. Remark. We remark, for the benefit of the more advanced student,

that ...

It should be noted that, although a statistic does not depend upon any

**unknown**parameter, the distribution of that statistic may very well depend upon

**unknown**parameters. Remark. We remark, for the benefit of the more advanced student,

that ...

Page 154

Suppose we are willing to accept as a fact that the outcome X of a random

experiment is a random variable that has a normal distribution with known

variance o” but

Suppose we are willing to accept as a fact that the outcome X of a random

experiment is a random variable that has a normal distribution with known

variance o” but

**unknown**mean p. That is, p. is some constant, but its value is**unknown**.Page 162

is a 95 per cent confidence interval for the ratio of/o3 of the two

variances. Example 3. If in the preceding discussion n = 10, m = 5, s? = 20.0, s3 =

35.6, then the interval 1 \ 5(35.6/4 5(35.6)/4 (#) IO(ZOO)75' (8.90) 10(20.0)/9 or (

0.4, ...

is a 95 per cent confidence interval for the ratio of/o3 of the two

**unknown**variances. Example 3. If in the preceding discussion n = 10, m = 5, s? = 20.0, s3 =

35.6, then the interval 1 \ 5(35.6/4 5(35.6)/4 (#) IO(ZOO)75' (8.90) 10(20.0)/9 or (

0.4, ...

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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