Introduction to Mathematical Statistics |
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Page 20
... = 0 and Pr ( X = 0 ) 0. More generally , if two probability density functions of random variables of the continuous type differ only on a set having probability zero , the two corresponding 20 [ Ch . 1 Distributions of Random Variables.
... = 0 and Pr ( X = 0 ) 0. More generally , if two probability density functions of random variables of the continuous type differ only on a set having probability zero , the two corresponding 20 [ Ch . 1 Distributions of Random Variables.
Page 56
... random variables of the 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 X1 and X2 . Take ...
... random variables of the 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 X1 and X2 . Take ...
Page 57
... type of random variable . It is called the conditional p.d.f. of the continuous type of random variable X2 , given that the continuous type of random variable X1 has the value x1 . When ƒ2 ( x2 ) > 0 , the conditional p.d.f. of the ...
... type of random variable . It is called the conditional p.d.f. of the continuous type of random variable X2 , given that the continuous type of random variable X1 has the value x1 . When ƒ2 ( x2 ) > 0 , the conditional p.d.f. of the ...
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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