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Page 86
... ( t ) = p [ 1 − ( 1 - p ) e ' ] ' . Find the mean and the variance of this distribution . - 3.13 . Let X and X2 have ... mx I = 0 x ! converges , for all values of m , to em . Consider the function f ( x ) defined by -m f ( x ) = me x ...
... ( t ) = p [ 1 − ( 1 - p ) e ' ] ' . Find the mean and the variance of this distribution . - 3.13 . Let X and X2 have ... mx I = 0 x ! converges , for all values of m , to em . Consider the function f ( x ) defined by -m f ( x ) = me x ...
Page 88
... m x ! for all real values of t . Since = M ' ( t ) and M " ( t ) = em ( et − 1 ) ( met ) , em ( et - 1 ) ( met ) + em ‹ et −1 ) ( met ) 2 , then μ = M ' ( 0 ) = m 88 [ Ch . 3 Some Special Distributions.
... m x ! for all real values of t . Since = M ' ( t ) and M " ( t ) = em ( et − 1 ) ( met ) , em ( et - 1 ) ( met ) + em ‹ et −1 ) ( met ) 2 , then μ = M ' ( 0 ) = m 88 [ Ch . 3 Some Special Distributions.
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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