Introduction to Mathematical Statistics |
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Page 153
... denote a random sample of size 10 from a distribution that is n ( μ , σ2 ) . Let Y = ( X , - ) 2 . What is the probability that the random interval ( Y / 20.5 , Y / 3.25 ) includes the point o2 ? We know that Y / o2 is x2 ( 10 ) ...
... denote a random sample of size 10 from a distribution that is n ( μ , σ2 ) . Let Y = ( X , - ) 2 . What is the probability that the random interval ( Y / 20.5 , Y / 3.25 ) includes the point o2 ? We know that Y / o2 is x2 ( 10 ) ...
Page 170
... random sample , are stochastically dependent . Example 1. Let X denote a random variable of the continuous type with p.d.f. f ( x ) which is positive and continuous , provided a < x < b , and is zero elsewhere . The distribution ...
... random sample , are stochastically dependent . Example 1. Let X denote a random variable of the continuous type with p.d.f. f ( x ) which is positive and continuous , provided a < x < b , and is zero elsewhere . The distribution ...
Page 272
... denote the order statistics of a random sample of size 4 from this distribution . Let the observed value of Y1 be y4 . We reject Ho : 0 = 1 and accept H1 : 0 1 if either y≤or y ≥ 1. Find the power function K ( 0 ) , 0 < 0 , of the ...
... denote the order statistics of a random sample of size 4 from this distribution . Let the observed value of Y1 be y4 . We reject Ho : 0 = 1 and accept H1 : 0 1 if either y≤or y ≥ 1. Find the power function K ( 0 ) , 0 < 0 , of the ...
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A₁ A₂ Accordingly c₁ chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval 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 hypothesis H₁ independent random variables integral joint p.d.f. k₁ Let the random Let X1 Let Y₁ likelihood ratio limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ Poisson distribution positive integer probability density functions probability set function 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 t₂ theorem unbiased statistic variance o² W₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ σ²