## Introduction to Mathematical Statistics |

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Page 152

The length is 40/Vn, a constant function of X; so the expected value of the length

of the random interval is 49/Vn.

assigned, we can make this length as short as we please by taking m sufficiently

large.

The length is 40/Vn, a constant function of X; so the expected value of the length

of the random interval is 49/Vn.

**Note**that we ... and**note**further that, for oassigned, we can make this length as short as we please by taking m sufficiently

large.

Page 239

Thus 1 < *[[o]}

and only when VWW) too." - evos () – 9). 66 that is, when and only when 8 ln g(y;

6 (2) *** - d.o.) - 9) where the constant c may depend upon 6 but not upon y.

Thus 1 < *[[o]}

**Note**that in accordance with Exercise 9.6, we have equality whenand only when VWW) too." - evos () – 9). 66 that is, when and only when 8 ln g(y;

6 (2) *** - d.o.) - 9) where the constant c may depend upon 6 but not upon y.

Page 366

[4] Carpenter, O., “

Variates,” Ann. Math. Stat., 21, 455 (1950). [5] Cochran, W. G., “The Distribution of

Quadratic Forms in a Normal System, with Applications to the Analysis of

Covariance ...

[4] Carpenter, O., “

**Note**on the Extension of Craig's Theorem to NoncentralVariates,” Ann. Math. Stat., 21, 455 (1950). [5] Cochran, W. G., “The Distribution of

Quadratic Forms in a Normal System, with Applications to the Analysis of

Covariance ...

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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