Introduction to Mathematical Statistics |
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Page 104
... mean μ2 + p ( σ2 / σ1 ) ( 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 o2 ( 1 - E ( Y x ) = μ2 + p ( x μι ) . 02 - 01 01 Since the ...
... mean μ2 + p ( σ2 / σ1 ) ( 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 o2 ( 1 - E ( Y x ) = μ2 + p ( x μι ) . 02 - 01 01 Since the ...
Page 148
... mean μ and variance o2 . The mean and the variance of Y = n n i Įk , X , are respectively μy = ( Σκ ) μ_and σε py = 1 1 n ( Σ k2 ) o2 . 1 Example 3. Let X = 1⁄2 , X1 / n denote the mean of a random sample of size n from a distribution ...
... mean μ and variance o2 . The mean and the variance of Y = n n i Įk , X , are respectively μy = ( Σκ ) μ_and σε py = 1 1 n ( Σ k2 ) o2 . 1 Example 3. Let X = 1⁄2 , X1 / n denote the mean of a random sample of size n from a distribution ...
Page 149
... mean and variance of the random variable X. Let Y = c + bX , where b and c are real constants . Show that the mean and the variance of Y are , respectively , c + bμ and b22 . 4.75 . A person rolls a die , tosses a coin , and draws a ...
... mean and variance of the random variable X. Let Y = c + bX , where b and c are real constants . Show that the mean and the variance of Y are , respectively , c + bμ and b22 . 4.75 . A person rolls a die , tosses a coin , and draws a ...
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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 F distribution function F(x given hypothesis H₁ 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 Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variables X₁ variance o² W₁ X₁ X₁ and X2 X₂ x²(n Y₂ Z₁ zero elsewhere μ₁ σ²