Introduction to Mathematical Statistics |
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Page 219
... probability density functions . So we could say we shall show that E [ u ( X ) ] : 0 for every > 0 requires u ( x ) = 0 at every point x at which at least one member of the family of probability density functions is positive . Our ...
... probability density functions . So we could say we shall show that E [ u ( X ) ] : 0 for every > 0 requires u ( x ) = 0 at every point x at which at least one member of the family of probability density functions is positive . Our ...
Page 220
... probability density functions is positive , then the family of probability density functions is called a complete family . Remarks . Two remarks should be made . On p . 35 it was noted that the existence of E [ u ( X ) ] implies that ...
... probability density functions is positive , then the family of probability density functions is called a complete family . Remarks . Two remarks should be made . On p . 35 it was noted that the existence of E [ u ( X ) ] implies that ...
Page 222
... probability density functions be complete . If there is a continuous function of Y1 which is an unbiased statistic for 0 , then this function of Y1 is the unique best statistic for 0. Here " unique " is used in the sense described in ...
... probability density functions be complete . If there is a continuous function of Y1 which is an unbiased statistic for 0 , then this function of Y1 is the unique best statistic for 0. Here " unique " is used in the sense described in ...
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A₁ A₂ accept accordance Accordingly alternative approximately assume called cent Chapter complete compute 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 H₁ Hence hypothesis 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 parameter 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 stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variables X1 variance W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁