## Introduction to mathematical statistics |

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Page 210

We shall show that Y4 is a sufficient

Y4 is 4' g(y1, y2, y3, y*; o) = ^ o < ^ < y2 < y3 < y4 < e, = 0 elsewhere, and the

p.d.f. of Y4 is g4(2/4;

...

We shall show that Y4 is a sufficient

**statistic**for 8. The joint p.d.f. of Y11, Y2, Y3,Y4 is 4' g(y1, y2, y3, y*; o) = ^ o < ^ < y2 < y3 < y4 < e, = 0 elsewhere, and the

p.d.f. of Y4 is g4(2/4;

**9**) - ^. 0 < y4 < 0, = 0 elsewhere. Accordingly, the conditional...

Page 215

On intuitive grounds, we might surmise that the conditional p.d.f. of Y2, given

some linear function aY1 + b, a / 0, of Y1, does not depend upon

seems as though the random variable aY1 + b is also a sufficient

On intuitive grounds, we might surmise that the conditional p.d.f. of Y2, given

some linear function aY1 + b, a / 0, of Y1, does not depend upon

**9**. That is, itseems as though the random variable aY1 + b is also a sufficient

**statistic**for 8.Page 218

sample from a distribution that has p.d.f. f(x;

u1(X1, X2,. . . , Xn) is a sufficient

. . , Xn) be another

sample from a distribution that has p.d.f. f(x;

**9**), de£l, where it is known that Y1 =u1(X1, X2,. . . , Xn) is a sufficient

**statistic**for the parameter**9**. Let Y2 = u2(X1, X2, .. . , Xn) be another

**statistic**(but not a function of Y1 alone) which is an unbiased ...### What people are saying - Write a review

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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