## 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

...

**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

...

Page 176

Robert V. Hogg, Allen Thornton Craig. 6.3. Let Yj < Y2 < Y3 be the

of a random sample of size 3 from the distribution having p.d.f. f(x) = e~{x~e\ 9 < x

< oo, zero elsewhere, where — oo < 9 < oo. Determine the function c(8) of 8 so ...

Robert V. Hogg, Allen Thornton Craig. 6.3. Let Yj < Y2 < Y3 be the

**order statistics**of a random sample of size 3 from the distribution having p.d.f. f(x) = e~{x~e\ 9 < x

< oo, zero elsewhere, where — oo < 9 < oo. Determine the function c(8) of 8 so ...

Page 182

Let Y1 < Y2 < Y3 < Y4 < Y6 denote the

5 from a distribution of the continuous type. Compute (a) PrfY, < f„ < Y8); (b) Pr(Y1

< f0.25 < Y3); (c) Pr (Y4 < £,80 < Y6). 6.17. Compute Pr (Y3 < f0-6 < Y7) if Y1 < ...

Let Y1 < Y2 < Y3 < Y4 < Y6 denote the

**order statistics**of a random sample of size5 from a distribution of the continuous type. Compute (a) PrfY, < f„ < Y8); (b) Pr(Y1

< f0.25 < Y3); (c) Pr (Y4 < £,80 < Y6). 6.17. Compute Pr (Y3 < f0-6 < Y7) if Y1 < ...

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Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere