## Introduction to Mathematical Statistics |

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Page 100

various values of k have been prepared and are partially reproduced in

in the Appendix. We use the notation (for normal) N(x) - so *****aw. thus, if X is n(

u, go), then P: € 4 x < c, - P. (*****) - P: (*****) Or or or or - N(**) — N **) Or Or It is

...

various values of k have been prepared and are partially reproduced in

**Table**IIIin the Appendix. We use the notation (for normal) N(x) - so *****aw. thus, if X is n(

u, go), then P: € 4 x < c, - P. (*****) - P: (*****) Or or or or - N(**) — N **) Or Or It is

...

Page 369

Robert V. Hogg.

|7.7 42.6 45.7 49.6 30 | 5.0 | 6.8 |8.5 43.8 47.0 50.9 * This

adapted from “

Robert V. Hogg.

**TABLE**II ... 43.2 47.0 28 |3.6 |5.3 | 6.9 4|.3 44.5 48.3 29 |4.3 | 6.0|7.7 42.6 45.7 49.6 30 | 5.0 | 6.8 |8.5 43.8 47.0 50.9 * This

**table**is abridged andadapted from “

**Tables**of Percentage Points of the Incomplete Beta Function and ...Page 371

2,052 2.473 2.77| 28 |.3|3 |.70| 2.048 2.467 2.763 29 | 3 || |.699 2,045 2.462 2.756

30 | 3 || 0 | .697 2,042 2.457 2.750 * This

...

**TABLE**IV The t Distribution* Pr (T • t) = ... |.706 2,056 2.479 2.779 27 |.3|4 |.7032,052 2.473 2.77| 28 |.3|3 |.70| 2.048 2.467 2.763 29 | 3 || |.699 2,045 2.462 2.756

30 | 3 || 0 | .697 2,042 2.457 2.750 * This

**table**is abridged from**Table**III of Fisher...

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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