## Introduction to Mathematical Statistics |

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Page 158

and s?, will provide a 95 per

variances of the two independent normal distributions are unknown but equal. A

consideration of the difficulty encountered when the unknown variances of the

two ...

and s?, will provide a 95 per

**cent**confidence interval for pi – pla when thevariances of the two independent normal distributions are unknown but equal. A

consideration of the difficulty encountered when the unknown variances of the

two ...

Page 162

is a 95 per

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 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, ...

Page 183

proper fraction p is exactly the same as the probability that the random interval (–

oo, X) contains no more than 100p per

X. We now refer to Theorem 2. Consider the difference Z, -Z = F(Y) — F(Y), i < j.

proper fraction p is exactly the same as the probability that the random interval (–

oo, X) contains no more than 100p per

**cent**of the probability for the distribution ofX. We now refer to Theorem 2. Consider the difference Z, -Z = F(Y) — F(Y), i < j.

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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