## Introduction to Mathematical Statistics |

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Page 180

Moreover, the joint p.d.f. of Z = F(Y) and Z, = F(Y) is, with i < j and in accordance

with

– 2)"-", 0 < z < z, * 1, = 0 elsewhere. We shall next define the concept of a ...

Moreover, the joint p.d.f. of Z = F(Y) and Z, = F(Y) is, with i < j and in accordance

with

**Equation**(3), Section 6.1, given by n! (2) hué o – FTTHIV-i x 2-1(z, - z)|-1-1 (1– 2)"-", 0 < z < z, * 1, = 0 elsewhere. We shall next define the concept of a ...

Page 181

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

obtained by a more direct argument. If we are to have Yo - 8, at least k items of

the random sample must be less than £,. Now Pr(X - 8,) = p, where X is an item of

the ...

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 Yo - 8, at least k items of

the random sample must be less than £,. Now Pr(X - 8,) = p, where X is an item of

the ...

Page 357

The latter

the sum of the matrices A1, ..., As exclusive of At. Let R. denote the rank of B.

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

the ...

The latter

**equation**implies that I = A1 + A2 + . . . + A*. Let B, - I — At. That is, B, isthe sum of the matrices A1, ..., As exclusive of At. Let R. denote the rank of B.

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

the ...

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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