Introduction to Mathematical Statistics |
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Page 143
... normal distribution with mean zero and variance one . Show that the moment - generating function E ( et ( UV ) of the product UV is ( 1 — t2 ) −1/2 , −1 < t < 1 . - - 4.56 . Let X and Y have a bivariate normal distribution with the ...
... normal distribution with mean zero and variance one . Show that the moment - generating function E ( et ( UV ) of the product UV is ( 1 — t2 ) −1/2 , −1 < t < 1 . - - 4.56 . Let X and Y have a bivariate normal distribution with the ...
Page 348
... normal distribution , where μ is the matrix of the means and V is the positive definite covariance matrix . Let Y c'X and Z d'X , where X ' = [ X1 ... Normal Distribution Theory [ Ch . 13 The Distributions of Certain Quadratic Forms.
... normal distribution , where μ is the matrix of the means and V is the positive definite covariance matrix . Let Y c'X and Z d'X , where X ' = [ X1 ... Normal Distribution Theory [ Ch . 13 The Distributions of Certain Quadratic Forms.
Page 381
... distribution function , 54 Joint probability density function , 54 Law of large numbers , 81 , 149 Lehmann - Scheffé ... normal distribution , 105 of chi - square distribution , 93 of gamma distribution , 92 of multinomial distribution ...
... distribution function , 54 Joint probability density function , 54 Law of large numbers , 81 , 149 Lehmann - Scheffé ... normal distribution , 105 of chi - square distribution , 93 of gamma distribution , 92 of multinomial distribution ...
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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