Introduction to Mathematical Statistics |
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Page 39
... a2 , az , .... E ( X ) = a1ƒ ( a1 ) + a2f ( a2 ) + açƒ ( a3 ) + ··· . This sum of products is seen to be a ... variance of X ( or the variance of the distribution ) . The variance of X will be denoted by o2 , and we define o2 , if it ...
... a2 , az , .... E ( X ) = a1ƒ ( a1 ) + a2f ( a2 ) + açƒ ( a3 ) + ··· . This sum of products is seen to be a ... variance of X ( or the variance of the distribution ) . The variance of X will be denoted by o2 , and we define o2 , if it ...
Page 133
... A2 = { ( x1 , X2 ) ; x2 < x1 } . Moreover , our transformation X2 now ... variance Y , of our random sample . An easy computation shows that J = 2 ... variance of our sample , is x2 ( 1 ) ; and the two are stochastically independent ...
... A2 = { ( x1 , X2 ) ; x2 < x1 } . Moreover , our transformation X2 now ... variance Y , of our random sample . An easy computation shows that J = 2 ... variance of our sample , is x2 ( 1 ) ; and the two are stochastically independent ...
Page 149
... variance of Z = 6 , P = 1 , μ2 = 3X 2Y . - = 4 , o = 4.72 . Let X and Y be stochastically independent random ... a2 , b1 , b2 , and the parameters of the distribution . Y = 1 4.80 . Let X1 , X2 , . . . , X , be a random sample of size n from ...
... variance of Z = 6 , P = 1 , μ2 = 3X 2Y . - = 4 , o = 4.72 . Let X and Y be stochastically independent random ... a2 , b1 , b2 , and the parameters of the distribution . Y = 1 4.80 . Let X1 , X2 , . . . , X , be a random sample of size n from ...
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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