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 . 02 t202 ( 1 tap με 02 exp { 122 - 12p 1/2 42 + ( 203 ( 1 = p2 ) } [ " _ exp [ ( 1 + tap 22 ) x ] / 1 ( x ) dx . 01 2 But E ( etx ) = exp [ μ1t + ( 02t2 ) / 2 ] for all real values ...
... Accordingly , M ( t1 , t2 ) can be written in the form . 02 t202 ( 1 tap με 02 exp { 122 - 12p 1/2 42 + ( 203 ( 1 = p2 ) } [ " _ exp [ ( 1 + tap 22 ) x ] / 1 ( x ) dx . 01 2 But E ( etx ) = exp [ μ1t + ( 02t2 ) / 2 ] for all real values ...
Page 170
... Accordingly , 12 h ( Y2 ) = 6ƒ ( Y2 ) svo su2 ƒ ( Y1 ) f ( Y3 ) dy , dyз , V2 = 6f ( y2 ) F ( Y2 ) [ 1 - F ( y2 ) ] , a < y2 < b , = 0 elsewhere . m Pr ( Y2 ≤ m ) = 6 [ ′′ { F ( y2 ) ƒ ( Y2 ) — [ F ( Y2 ) ] 2ƒ ( Y2 ) } dy2 = m 1 6 ...
... Accordingly , 12 h ( Y2 ) = 6ƒ ( Y2 ) svo su2 ƒ ( Y1 ) f ( Y3 ) dy , dyз , V2 = 6f ( y2 ) F ( Y2 ) [ 1 - F ( y2 ) ] , a < y2 < b , = 0 elsewhere . m Pr ( Y2 ≤ m ) = 6 [ ′′ { F ( y2 ) ƒ ( Y2 ) — [ F ( Y2 ) ] 2ƒ ( Y2 ) } dy2 = m 1 6 ...
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Common terms and phrases
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