Dr. Hackney STA Solutions pg 40

Dr. Hackney STA Solutions pg 40 - Second Edition 3-13 c.(i)...

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Unformatted text preview: Second Edition 3-13 c.(i) h ( x ) = 1 x I { <x< } ( x ) , c ( ) = ( ) > , w 1 ( ) = , w 2 ( ) = , t 1 ( x ) = log( x ) , t 2 ( x ) =- x . (ii) A line. d.(i) h ( x ) = C exp( x 4 ) I {- <x< } ( x ) , c ( ) = exp( 4 )- < < , w 1 ( ) = , w 2 ( ) = 2 , w 3 ( ) = 3 , t 1 ( x ) =- 4 x 3 , t 2 ( x ) = 6 x 2 , t 3 ( x ) =- 4 x . (ii) The curve is a spiral in 3-space. (iii) A good picture can be generated with the Mathematica statement ParametricPlot3D[{t, t^2, t^3}, {t, 0, 1}, ViewPoint -> {1, -2, 2.5}]. 3.35 a. In Exercise 3.34(a) w 1 ( ) = 1 2 and for a n( e ,e ), w 1 ( ) = 1 2 e . b. E X = = , then = . Therefore h ( x ) = 1 x I { <x< } ( x ) , c ( ) = ( )( ) , > , w 1 ( ) = , w 2 ( ) = , t 1 ( x ) = log( x ) , t 2 ( x ) =- x . c. From (b) then ( 1 ,..., n , 1 ,..., n ) = ( 1 ,..., n , 1 ,..., n ) 3.37 The pdf ( 1 ) f (...
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