Introduction to Mathematical Statistics |
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Page 22
... zero elsewhere . ( b ) f ( x ) = -x cxe ̄x , 0 < x < ∞ , zero elsewhere . 1.28 . Let f ( x ) = x / 15 , x = 1 , 2 , 3 , 4 , 5 , zero elsewhere , be the p.d.f. of X. Find Pr [ X = 1 or 2 ] , Pr [ } < X < { ] , and Pr [ 1 ≤ X ≤ 2 ] ...
... zero elsewhere . ( b ) f ( x ) = -x cxe ̄x , 0 < x < ∞ , zero elsewhere . 1.28 . Let f ( x ) = x / 15 , x = 1 , 2 , 3 , 4 , 5 , zero elsewhere , be the p.d.f. of X. Find Pr [ X = 1 or 2 ] , Pr [ } < X < { ] , and Pr [ 1 ≤ X ≤ 2 ] ...
Page 29
... 0 , zero elsewhere . = = ( b ) f ( x ) ( c ) f ( x ) ( d ) f ( x ) ( e ) f ( x ) = = } , x = -1 , 0 , 1 , zero elsewhere . x / 15 , x = 1 , 2 , 3 , 4 , 5 , zero elsewhere . 3 ( 1 − x ) 2 , 0 < x < 1 , zero elsewhere . 1 / x2 , 1 < x < ∞ , ...
... 0 , zero elsewhere . = = ( b ) f ( x ) ( c ) f ( x ) ( d ) f ( x ) ( e ) f ( x ) = = } , x = -1 , 0 , 1 , zero elsewhere . x / 15 , x = 1 , 2 , 3 , 4 , 5 , zero elsewhere . 3 ( 1 − x ) 2 , 0 < x < 1 , zero elsewhere . 1 / x2 , 1 < x < ∞ , ...
Page 176
... 0 < x < ∞ , zero elsewhere , where -∞ << ∞ . Determine the function c ( 0 ) of @ so that Pr [ 0 < Y1 < c ( 0 ) ] = 0.95 . From this result show how to construct a 95 per cent confidence interval for 0 . = 6.4 . In Example 4 of this ...
... 0 < x < ∞ , zero elsewhere , where -∞ << ∞ . Determine the function c ( 0 ) of @ so that Pr [ 0 < Y1 < c ( 0 ) ] = 0.95 . From this result show how to construct a 95 per cent confidence interval for 0 . = 6.4 . In Example 4 of this ...
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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