## Introduction to Mathematical Statistics |

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Page 151

Robert V. Hogg. C H A P T E R 5

random

2.

Robert V. Hogg. C H A P T E R 5

**Interval**Estimation 5.1 Random**Intervals**An**interval**, at least one of whose end points is a random variable, will be called arandom

**interval**. Let X denote a random variable and consider the event 1 < X →2.

Page 153

What is the probability l that the random

point g”? We know that Y/o” is x*(10). Moreover, the events Y/20.5 - go & Y/3.25

and 3.25 × Y/o” < 20.5 are equivalent. Accordingly, the probability that our

random ...

What is the probability l that the random

**interval**(Y/20.5, Y/3.25) includes thepoint g”? We know that Y/o” is x*(10). Moreover, the events Y/20.5 - go & Y/3.25

and 3.25 × Y/o” < 20.5 are equivalent. Accordingly, the probability that our

random ...

Page 162

is a 95 per cent confidence

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

35.6, then the

0.4, ...

is a 95 per cent confidence

**interval**for the ratio of/o3 of the two unknownvariances. 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