Introduction to Mathematical Statistics |
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Page 109
... random sample from the normal distribution under consideration . Once the holes have been drilled and the diameters measured , the 20 numbers may be used , as will be seen later , to elicit information about and o2 . μ The term " random ...
... random sample from the normal distribution under consideration . Once the holes have been drilled and the diameters measured , the 20 numbers may be used , as will be seen later , to elicit information about and o2 . μ The term " random ...
Page 153
... random sample of size 10 from a 10 Σ i distribution that is n ( μ , o2 ) . Let Y = ( X , - μ ) 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 ) ...
... random sample of size 10 from a 10 Σ i distribution that is n ( μ , o2 ) . Let Y = ( X , - μ ) 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 176
... random sample of size 5 from this distribution is 5 5 81 ( 91 ) = ( - ) - ( -9 ) , y1 = 1 , 2 , ... , 6 , · * ° zero elsewhere . Note that in this exercise the random sample is from a distribution of the discrete type . All formulas in ...
... random sample of size 5 from this distribution is 5 5 81 ( 91 ) = ( - ) - ( -9 ) , y1 = 1 , 2 , ... , 6 , · * ° zero elsewhere . Note that in this exercise the random sample is from a distribution of the discrete type . All formulas in ...
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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