Introduction to Mathematical Statistics |
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Page 39
... mean value of X ( or the mean value of the distribution ) . The mean value μ of a random variable X is defined , when it exists , to be μ E ( X ) , whether X is a random variable of the discrete or of the continuous type . = Another ...
... mean value of X ( or the mean value of the distribution ) . The mean value μ of a random variable X is defined , when it exists , to be μ E ( X ) , whether X is a random variable of the discrete or of the continuous type . = Another ...
Page 104
... mean μ2 + p ( 02/01 ) ( x − μ1 ) and variance p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y , given X = x , is linear in x and is given by 02 E ( Y❘x ) = με + ρ - ( 2 μι ) . 01 P 01 Since the ...
... mean μ2 + p ( 02/01 ) ( x − μ1 ) and variance p2 ) . Thus , with a bivariate normal distribution , the conditional mean of Y , given X = x , is linear in x and is given by 02 E ( Y❘x ) = με + ρ - ( 2 μι ) . 01 P 01 Since the ...
Page 149
... mean and variance of Z 4.72 . Let X and Y be stochastically independent random variables with means μ1 , μ2 and ... mean and variance of the random variable X. Let Y = c + bX , where b and c are real constants . Show that the mean and ...
... mean and variance of Z 4.72 . Let X and Y be stochastically independent random variables with means μ1 , μ2 and ... mean and variance of the random variable X. Let Y = c + bX , where b and c are real constants . Show that the mean and ...
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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