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# sol12 - 769!Xf 2" 0 e(d U 9!XY 2 0 e(d U%U" [email protected] 0...

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Unformatted text preview: 769#!Xf 2 " 0 e(d U 9#!XY 2 0 e(d U %U " X % #@Y 0 [email protected] U % G U %U " % a %U G U USIG X % `#!Y 0 % VW( 1TRQPH FE 4"!3D !X C D # " @ 9" % # " B 9"A % # " B "8 % # " B "4 % # " "&A # " " # " B " # " B 9" A # 2 # " @ 9" 8 . The other one is similar. 76#5# 4"!3 2 " 0 ) ! ' ' ( 5## 4"!3 2 1) ' ' 0( &%\$## "! Solutions for Homework 12 . Then where since The solution follows by setting these equal to 0. (2) (3) The log-density is (1) Let . The second derivatives are 1 U E ' % !' ' U E ' % ' ' ! E ' % ' ' %E %U '' %E % '' %E % ' ' % 6 C C " # \$ % ' " # % & \$ 6 C This is the same as the exact expression for the variance. # 6 % # " U " T( ( % is !( C % " \$ # %' " # % & \$ C C # U !5 Now we need the inverse Take minus one times the expected value to get Now, the approximate variance of 2 C ! ...
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