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 accept accordance Accordingly alternative approximately assume called cent Chapter complete compute Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given H₁ Hence hypothesis inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics parameter probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variables X1 variance W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁