Introduction to Mathematical Statistics |
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Page 115
... problem when the random variables are of the continuous type . It is again helpful to begin with a special problem . Example 1. Let X be a random variable of the Sect . 4.3 ] Transformations of Variables of the Continuous Type 115 ...
... problem when the random variables are of the continuous type . It is again helpful to begin with a special problem . Example 1. Let X be a random variable of the Sect . 4.3 ] Transformations of Variables of the Continuous Type 115 ...
Page 158
... problem of finding a confidence interval for the differ- ence μ1 με between the two means of two independent normal distributions if the variances of and o2 are known but not necessarily equal . - 5.11 . Discuss Exercise 5.10 when it is ...
... problem of finding a confidence interval for the differ- ence μ1 με between the two means of two independent normal distributions if the variances of and o2 are known but not necessarily equal . - 5.11 . Discuss Exercise 5.10 when it is ...
Page 282
... problem is defined in Section 9.4 as a w ( y ) such that E [ ( 0 , w ( y ) ) | Y = y ] is a minimum . In this problem if w = 0 ' , the conditional expectation of ( 0 , w ) , given X1 = x1 ,. Xn .... = Xn ' is ΣL ( 0,0 ' ) k ( 0 | X2 ...
... problem is defined in Section 9.4 as a w ( y ) such that E [ ( 0 , w ( y ) ) | Y = y ] is a minimum . In this problem if w = 0 ' , the conditional expectation of ( 0 , w ) , given X1 = x1 ,. Xn .... = Xn ' is ΣL ( 0,0 ' ) k ( 0 | X2 ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ