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Page 135
... xn ) denote the joint p.d.f. of the n random vari- ables X1 , X2 , ... , X. These random variables may or may not be the items of a random sample from some distribution that has a given p.d.f. f ( x ) . Let Y1 = u1 ( X1 , X2 , ... , Xn ) ...
... xn ) denote the joint p.d.f. of the n random vari- ables X1 , X2 , ... , X. These random variables may or may not be the items of a random sample from some distribution that has a given p.d.f. f ( x ) . Let Y1 = u1 ( X1 , X2 , ... , Xn ) ...
Page 147
... denote a random variable with mean μ , and variance o ?, i = 1 , 2 , . . . , n . Let X1 , X2 , ... , X2 be mutually ... ( Xn ) n = knμn + kata = 1⁄2 katı Σκιμι k11 + k2μ2 + The variance of Y is given by = = = = 1 E { [ ( k1X1 + + knXn ) - ( ...
... denote a random variable with mean μ , and variance o ?, i = 1 , 2 , . . . , n . Let X1 , X2 , ... , X2 be mutually ... ( Xn ) n = knμn + kata = 1⁄2 katı Σκιμι k11 + k2μ2 + The variance of Y is given by = = = = 1 E { [ ( k1X1 + + knXn ) - ( ...
Page 148
... Xn denote the items of a random sample of size n from a distribution that has mean μ and variance o2 . The mean and n the variance of Y = k‚X , are respectively μy = L Example 3. Let X = n 1 n py ( Σki ) μ and o } = Σ X , / n denote the ...
... Xn denote the items of a random sample of size n from a distribution that has mean μ and variance o2 . The mean and n the variance of Y = k‚X , are respectively μy = L Example 3. Let X = n 1 n py ( Σki ) μ and o } = Σ X , / n denote 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