Introduction to Mathematical Statistics |
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Page 16
... discrete type and the continuous type . For simplicity of presentation , we first consider a distribution of one random variable . ( a ) The discrete type of random variable . Let the outcome of a ran- dom experiment be represented by ...
... discrete type and the continuous type . For simplicity of presentation , we first consider a distribution of one random variable . ( a ) The discrete type of random variable . Let the outcome of a ran- dom experiment be represented by ...
Page 17
... discrete type and the continuous type . For simplicity of presentation , we first consider a distribution of one random variable . ( a ) The discrete type of random variable . Let the outcome of a ran- dom experiment be represented by ...
... discrete type and the continuous type . For simplicity of presentation , we first consider a distribution of one random variable . ( a ) The discrete type of random variable . Let the outcome of a ran- dom experiment be represented by ...
Page 56
... discrete type which have the joint p.d.f. f ( x1 , x2 ) that is positive on and is zero elsewhere . Let f1 ( x1 ) and ƒ2 ( x2 ) denote respectively the marginal probability density func- tions of X and X2 . Take A1 to be the set A1 ...
... discrete type which have the joint p.d.f. f ( x1 , x2 ) that is positive on and is zero elsewhere . Let f1 ( x1 ) and ƒ2 ( x2 ) denote respectively the marginal probability density func- tions of X and X2 . Take A1 to be the set A1 ...
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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