Introduction to Mathematical Statistics |
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Page 39
... a2 , aз , ... , then E ( X ) = a1ƒ ( a1 ) + a2f ( a2 ) + a3f ( 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 ...
... a2 , aз , ... , then E ( X ) = a1ƒ ( a1 ) + a2f ( a2 ) + a3f ( 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 ...
Page 133
... A2 = { ( x1 , X2 ) ; X2 < x1 } . Moreover , our transformation now defines a ... variance Y2 of our random sample . An easy computation shows that | J1 ... variance of our sample , is x2 ( 1 ) ; and the two are stochastically independent ...
... A2 = { ( x1 , X2 ) ; X2 < x1 } . Moreover , our transformation now defines a ... variance Y2 of our random sample . An easy computation shows that | J1 ... variance of our sample , is x2 ( 1 ) ; and the two are stochastically independent ...
Page 149
... variance of Z 4.72 . Let X and Y be stochastically independent random variables with means μ1 , μ2 and variances o2 ... a2 , b1 , b2 , and the parameters of the distribution . Y = 4.80 . Let X1 , X2 , . . . , X , be a random sample of size n ...
... variance of Z 4.72 . Let X and Y be stochastically independent random variables with means μ1 , μ2 and variances o2 ... a2 , b1 , b2 , and the parameters of the distribution . Y = 4.80 . Let X1 , X2 , . . . , X , be a random sample of size n ...
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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