{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

st422%20hw08%20solution

# st422%20hw08%20solution - Homework 8 Solutions 1 1 1 2 1...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Homework 8: Solutions 1 1 1 2 1 exp(-y/ ) y exp(- / ) 1 2 2 2 9.73: f ( ) y< L( ) f(y , ... | ) ln L = -nln ln L ˆ This is the MVUE of and since is a one-to-one function of , is the n i i n n i i n i i n i i y n y y n y n y y y d dx y y θ θ θ θ θ θ θ θ θ θ θ θ θ θ = = = =- = ≤ ∞ ∑ = = ∑- ∑ = ⇒ + = ∑ = = 2 MLE of which is not the MVUE of θ θ 2 2 1 1 2 1 1 1 1 1 1 2 120 130 128 2 2 3 2 9.76: a) f(y| ) exp( / ) y>0 L( ) exp( / ) ln L=-2nln ln ln L ˆ 63 b) Clearly, Y Gamma( 2, ) Thus E(Y)= 2 V(Y)= n n i i n i i n i i n n i i i i y n i i y n y n y y y y y d dx θ θ θ θ θ θ θ θ θ θ θ α β θ αβ θ αβ = = = = = =- + + × =- =- ∑ +- ∑ = + = ∑ ⇒ = = = = = = = ∑ ∏ ∑ ∼ 1 2 2 2 1 2 2 2 2 2 (2 ) 1 2 2 1 (2 ) 1 2 2 6 4 4 1 ˆ 2 130 6 6 2 2 ˆ E( ) E E( ) ˆ V( ) V V( ) c) ˆ ˆ Bound for the error of estimation=2 2 V( ) 2 106.14 d) MLE of V(Y)=MLE of 2 n i i n i i y n n i n n i y n n i n n n n i p y y θ θ θ θ θ θ θ θ θ θ σ θ θ = = = = × ∑ = = = = ∑ = = = = = = = = ≈ ∑ ∑ 2 2 ˆ 2 (By Invariance property of MLEs) 2(130 ) 7938 MLE θ = = = 1 2 1 1 ( ) 1 1 ( ) 1 1 1 1 1 2 1 9.77 : f(y| , ) exp( / ) y>0 L( ) exp( / ) ln L=-nln ( ) n ln +ln / ln L / ˆ b) ˆ E( ) ˆ V( )...
View Full Document

{[ snackBarMessage ]}

### Page1 / 8

st422%20hw08%20solution - Homework 8 Solutions 1 1 1 2 1...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online