Dr. Hackney STA Solutions pg 40

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

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Unformatted text preview: Second Edition 3-13 c.(i) h ( x ) = 1 x I { <x< ∞} ( x ) , c ( α ) = α α Γ( α ) α > , w 1 ( α ) = α, w 2 ( α ) = α, t 1 ( x ) = log( x ) , t 2 ( x ) =- x . (ii) A line. d.(i) h ( x ) = C exp( x 4 ) I {-∞ <x< ∞} ( x ) , c ( θ ) = exp( θ 4 )- ∞ < θ < ∞ , w 1 ( θ ) = θ, w 2 ( θ ) = θ 2 , w 3 ( θ ) = θ 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 ( λ ) = 1 2 λ and for a n( e θ ,e θ ), w 1 ( θ ) = 1 2 e θ . b. E X = μ = αβ , then β = μ α . Therefore h ( x ) = 1 x I { <x< ∞} ( x ) , c ( α ) = α α Γ( α )( μ α ) α ,α > , w 1 ( α ) = α, w 2 ( α ) = α μ , t 1 ( x ) = log( x ) , t 2 ( x ) =- x . c. From (b) then ( α 1 ,...,α n ,β 1 ,...,β n ) = ( α 1 ,...,α n , α 1 μ ,..., α n μ ) 3.37 The pdf ( 1 σ ) f (...
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