## Introduction to Mathematical Statistics |

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Page 168

properties of such a statistic. These statistics have in recent times come to play an

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**Order Statistics**6.1 Distributions of**Order Statistics**In this section the notion of an**order statistic**will be defined and we shall investigate some of the simplerproperties of such a statistic. These statistics have in recent times come to play an

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Page 176

Let Y, & Ya & Ya be the

distribution having p.d. f. f(x) = e-o-'), 0 < r < co, zero elsewhere, where —oo & 0 <

oo. Determine the function c(6) of 6 so that Pr[6 : Yi < c(6)] = 0.95. From this result

...

Let Y, & Ya & Ya be the

**order statistics**of a random sample of size 3 from thedistribution having p.d. f. f(x) = e-o-'), 0 < r < co, zero elsewhere, where —oo & 0 <

oo. Determine the function c(6) of 6 so that Pr[6 : Yi < c(6)] = 0.95. From this result

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Page 182

Let Y, & Ya • Ya - Y, & Ys denote the

from a distribution of the continuous type. Compute (a) Pr(Yi < $o.5 × Ys); (b) Pr(

Yi < $o.25 × Ya); (c) Pr(Y, & £o.so 3 Ys). 6.17. Compute Pr(Ya • fols < Yo) if Yi < .

Let Y, & Ya • Ya - Y, & Ys denote the

**order statistics**of a random sample of size 5from a distribution of the continuous type. Compute (a) Pr(Yi < $o.5 × Ys); (b) Pr(

Yi < $o.25 × Ya); (c) Pr(Y, & £o.so 3 Ys). 6.17. Compute Pr(Ya • fols < Yo) if Yi < .

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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