Unformatted text preview: 4.26 with 1 /λ = α and 1 /μ = β . By independence, the joint distribution is the pdf f Z times the pmf f W , where f Z ( z  α,β ) = ( α + β ) e( α + β ) z , z ∈ (0 , ∞ ) , f W ( w  α,β ) = wα + (1 − w ) β α + β , w = 0 , 1 . 7.19 Here, σ 2 is the same for all the ǫ i . Note that Y i ∼ normal( βx i ,σ 2 ), so f Y i ( y i ) = 1 √ 2 πσ exp ± − ( y i − βx i ) 2 2 σ 2 ² . (a) Begin by writing f v Y ( vy  β,σ 2 ), and then use the factorization theorem. (b) Use the log likelihood. The MLE is a linear combination of Y i , so the expected value is easy to ²nd. (c) See the hint for (b)....
View
Full
Document
This note was uploaded on 11/29/2011 for the course MATH 4056 taught by Professor Staff during the Fall '08 term at LSU.
 Fall '08
 Staff
 Statistics

Click to edit the document details