Introduction to Mathematical Statistics |
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Page 40
... moment - generating function of a random variable X. Suppose there is a positive number h such that for −h < t < h ... moment - generating function of X ( or of the distribution ) and is denoted by M ( t ) . That is , M ( t ) = E ( etx ) ...
... moment - generating function of a random variable X. Suppose there is a positive number h such that for −h < t < h ... moment - generating function of X ( or of the distribution ) and is denoted by M ( t ) . That is , M ( t ) = E ( etx ) ...
Page 73
... moment - generating function of the joint distribution factors into the product of the moment - generating functions of the two marginal distributions . Suppose next that the moment - generating function of the joint distribution of X ...
... moment - generating function of the joint distribution factors into the product of the moment - generating functions of the two marginal distributions . Suppose next that the moment - generating function of the joint distribution of X ...
Page 193
Robert V. Hogg, Allen Thornton Craig. 7.3 Limiting Moment - Generating Functions To find the limiting distribution function of a random variable Y by use of the definition of limiting distribution function obviously requires that we know ...
Robert V. Hogg, Allen Thornton Craig. 7.3 Limiting Moment - Generating Functions To find the limiting distribution function of a random variable Y by use of the definition of limiting distribution function obviously requires that we know ...
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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