Introduction to Mathematical Statistics |
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Page 27
... Accordingly , the corresponding distribu- tion is neither of the continuous type nor of the discrete type . It may be described as a mixture of those types . F ( x ) 1 1 FIGURE 1.5 X = We shall now point out an important fact about a ...
... Accordingly , the corresponding distribu- tion is neither of the continuous type nor of the discrete type . It may be described as a mixture of those types . F ( x ) 1 1 FIGURE 1.5 X = We shall now point out an important fact about a ...
Page 105
... Accordingly , M ( t1 , t2 ) can be written in the form exp { 12442 02 t202 ( 1 - t2p με + 2 01 But E ( etx ) = ∞ 2 _p2 ) } [ " __ exp [ ( 1 + lap 2 ) = ] / 1 ( x ) dx . -∞ 01 / exp [ μ1t + ( o ? t2 ) / 2 ] for all real values of t ...
... Accordingly , M ( t1 , t2 ) can be written in the form exp { 12442 02 t202 ( 1 - t2p με + 2 01 But E ( etx ) = ∞ 2 _p2 ) } [ " __ exp [ ( 1 + lap 2 ) = ] / 1 ( x ) dx . -∞ 01 / exp [ μ1t + ( o ? t2 ) / 2 ] for all real values of t ...
Page 152
... Accordingly , the probability that the random interval ( | X | , | 10X ) includes the point o is σ X Pr ( i < | X | < 0 ) = 2 Pr ( 1 < < 1 ) 10 = - 2 [ N ( 1 ) N ( 0.1 ) ] = 0.60 , approximately . The length of the random interval is 9 ...
... Accordingly , the probability that the random interval ( | X | , | 10X ) includes the point o is σ X Pr ( i < | X | < 0 ) = 2 Pr ( 1 < < 1 ) 10 = - 2 [ N ( 1 ) N ( 0.1 ) ] = 0.60 , approximately . The length of the random interval is 9 ...
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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