## Introduction to mathematical statistics |

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Page 180

0 < z < 1, the marginal p.d.f. of Zk = F(Yk) is, according to

6.1, the following beta p.d.f. (1) K(zk) = n _ l)\(n - igi1*~1^ ~ ^n_fc' o < 2* < i. = 0

elsewhere. Moreover, the joint p.d.f. of Z< = i^Yj) and Z, = F(Yy) is, with i < j and in

...

0 < z < 1, the marginal p.d.f. of Zk = F(Yk) is, according to

**Equation**(2), Section6.1, the following beta p.d.f. (1) K(zk) = n _ l)\(n - igi1*~1^ ~ ^n_fc' o < 2* < i. = 0

elsewhere. Moreover, the joint p.d.f. of Z< = i^Yj) and Z, = F(Yy) is, with i < j and in

...

Page 181

It is interesting to observe that the right-hand member of

obtained by a more direct argument. If we are to have Yk < £p, at least k items of

the random sample must be less than f„. Now Pr (X < £p) = p, where X is an item

of ...

It is interesting to observe that the right-hand member of

**Equation**(4) can beobtained by a more direct argument. If we are to have Yk < £p, at least k items of

the random sample must be less than f„. Now Pr (X < £p) = p, where X is an item

of ...

Page 357

The latter

the sum of the matrices A1, . . . , Ak exclusive of A,. Let Rt denote the rank of B(.

Since the rank of the sum of several matrices is less than or equal to the sum of ...

The latter

**equation**implies that I = K1 + A2 + . . . + Afc. Let B, = I — Aj. That is, B, isthe sum of the matrices A1, . . . , Ak exclusive of A,. Let Rt denote the rank of B(.

Since the rank of the sum of several matrices is less than or equal to the sum of ...

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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