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Page 142
... X1 and X2 . -- 1 = E ( et ( x1 + x2 ) and = 4.46 . Let the stochastically independent random variables X1 and X2 have binomial distributions with parameters n1 , P1and n2 , P2 , respectively . Show that Y = X1 - X2 + n2 has a binomial ...
... X1 and X2 . -- 1 = E ( et ( x1 + x2 ) and = 4.46 . Let the stochastically independent random variables X1 and X2 have binomial distributions with parameters n1 , P1and n2 , P2 , respectively . Show that Y = X1 - X2 + n2 has a binomial ...
Page 143
... Let Y = X1 + X2 and Z = X2 + X2 . Show that the moment- generating function of the joint distribution of Y and Z is for ― E { exp [ t1 ( X1 + X2 ) + t2 ( X } + X3 ) ] } = exp [ t2 / ( 1 1 - 2t2 - 2t2 ) ] -∞∞ < t1 < ∞ , ∞ < t2 ...
... Let Y = X1 + X2 and Z = X2 + X2 . Show that the moment- generating function of the joint distribution of Y and Z is for ― E { exp [ t1 ( X1 + X2 ) + t2 ( X } + X3 ) ] } = exp [ t2 / ( 1 1 - 2t2 - 2t2 ) ] -∞∞ < t1 < ∞ , ∞ < t2 ...
Page 149
... Let X and Y be random variables with μ1 . Find the mean and variance of Z = = 3X - 1 , Ма = 2Y . 4 , o 4 , = 4.72 ... X1 , X2 , ... , X , be a random sample of size n from a distribu- tion with mean μ μ and variance o2 . Show that E ( S2 ) = ...
... Let X and Y be random variables with μ1 . Find the mean and variance of Z = = 3X - 1 , Ма = 2Y . 4 , o 4 , = 4.72 ... X1 , X2 , ... , X , be a random sample of size n from a distribu- tion with mean μ μ and variance o2 . Show that E ( S2 ) = ...
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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