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solution6 - Solution of homework 6 1 ΦYY s = φYY(τ...

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Solution of homework 6 1. ( ) ( ) ( ) ( ) ( ) ( ) ( ) * exp exp YY YY XX s s d h h s d d d φ τ τ τ φ τ ξ σ ξ σ τ ξ σ τ Φ = = + ∫∫∫ Let γ τ ξ σ = + ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) * * * * * * * * exp exp exp exp exp exp exp exp exp exp YY XX XX XX XX XX s h h s d d d s d h s d h s d s d h s d h s d s d h s d h s d s H s H s φ γ ξ σ γ ξ σ ξ σ γ φ γ γ γ ξ ξ ξ σ σ σ φ γ γ γ ξ ξ ξ σ σ σ φ γ γ γ ξ ξ ξ σ σ σ Φ = + = = = − − = Φ ∫∫∫ ( ) ( ) ( ) ( ) ( ) ( ) ( ) * exp 2 exp 2 YY YY YY S f j f d h h j f d d d φ τ π τ τ φ τ ξ σ ξ σ π τ ξ σ τ = = + ∫∫∫ Let γ τ ξ σ = + ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) * * * 2 * exp 2 exp 2 exp 2 exp 2 exp 2 exp 2 exp 2 ˆ ˆ ˆ YY YY XX XX XX XX S f h h j f d d d j f d h j f d h j f d j f d h j f d h j f d S f H f H f S f H f φ γ ξ σ π γ ξ σ ξ σ γ φ γ π γ γ ξ π ξ ξ σ π σ σ φ γ π γ γ ξ π ξ ξ σ π σ σ = + = = = = ∫∫∫
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