Introduction to Mathematical Statistics |
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Page 74
... independence of X1 and X2 is generalized to the mutual stochastic independence of X1 , X2 , ... , Xn as follows : The random variables X1 , X2 , ... , X , are said to be mutually stochastically independent if and only if f ( x1 , X2 ...
... independence of X1 and X2 is generalized to the mutual stochastic independence of X1 , X2 , ... , Xn as follows : The random variables X1 , X2 , ... , X , are said to be mutually stochastically independent if and only if f ( x1 , X2 ...
Page 142
... independent random variables . Let X and Y = X1 + X2 have chi - square distributions with r1 and r degrees of freedom respectively . Here 1 < r . Show that X2 has a chi - square distribu- tion with r r1 degrees of freedom . Hint . Write ...
... independent random variables . Let X and Y = X1 + X2 have chi - square distributions with r1 and r degrees of freedom respectively . Here 1 < r . Show that X2 has a chi - square distribu- tion with r r1 degrees of freedom . Hint . Write ...
Page 149
... independent random variables with means μ1 , μ2 and variances o2 , o2 . Determine the correlation coefficient of X and Z = X Y in terms of μ1 , μ2 , 03 , 02 . ― 4.73 . Let X and Y be random variables with means μ1 ... Random Variables 149.
... independent random variables with means μ1 , μ2 and variances o2 , o2 . Determine the correlation coefficient of X and Z = X Y in terms of μ1 , μ2 , 03 , 02 . ― 4.73 . Let X and Y be random variables with means μ1 ... Random Variables 149.
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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