Fall_2005_Exam_C_solutions - FALL 2005 EXAM C SOLUTIONS...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: FALL 2005 EXAM C SOLUTIONS Question #1 Key: D (300) 3/10 S = (there are three observations greater than 300) (300) ln[ (300)] ln(0.3) 1.204 H S = = = . Question #2 Key: A 2 ( | ) ( | ) ( ) ; ( ) ; / 1/ 1/ 1 1 0.15 (1) 1 1 1 2 1 4 0.20 (2) 2 1 2 1 2 1 From the first equation, 0.15 0.15 and so 0.15 0.85 Then the second equat E X Var X v E a Var k v a n n Z n n = = = = = = = = = = = + + + = + = + + + + = + = + + + + = + = ion becomes 0.4 0.2 4 0.15 0.85 0.05 2.75 ; 0.01818 + = + = = Question #3 Key: E 1 1 0.75 ; 0.25 1 (100/ ) 1 (500/ ) (100/ ) 1/3; (500/ ) 3 = = + + = = Taking the ratio of these two equalities produces 5 9 = . From the second equality, 2 2 9 [(500/ ) ] 5 ; (500/ ) 5; 223.61 = = = = Question #4 Key: B 2 3 ( ) ( ) 2 ( 2 ) 2 4 8 1 ' ( ) 24 ''(2) 2 12 ; 12 6 f x a bx cx dx f a f a b c d f b f c d c d = + + + = = = = + + + = = = = + = Insert the values for a , b , and c into the second equation to obtain 2 2 4( 12 6 ) 8 ; 48 16 ; 3 d d d d = + + = = Then 6 c = and 2 3 ( ) 6 3 ; (1) 4 f x x x x f = + = Question #5 Key: E Begin with y 350 500 1000 1200 1500 s 2 2 1 1 1 r 10 8 5 2 1 Then 1 8 6 4 1 (1250) 0.24 10 8 5 2 S = = The likelihood function is 2 2 2 1 350/ 1 500/ 500/ 1 1000/ 1000/ 1 1200/ 1 1500/ 7 7900/ 2 1250(7)/7900 2 ( ) 7900 7 7900 ( ) 7ln ; '( ) 0; 7900/ 7 (1250) 0.33 L e e e e e e e e l l S e = = = = + = = = = The absolute difference is 0.09. Question #6 Key: E 4 2 2 3 4 4 4 1 2 2 2 3 2 2 3 2 2 2 2 3 2 5 2 2 4 2 4 2 4 2 2 4 ( ) '( ) ( ) 4(2) 4(4) 128 ( ) (2) (4) (4) ( 2 ) ( 4 ) ( 4 ) ( 4) ( 16) ( ) ln128 12ln 3ln( 4) 5ln( 16) 12 6 10 '( ) 0;12( 20 64) 6( 16 ) 10( 4 4 1 6 x f x S x x L f f S l l = = + = = = + + + + + = + + + = = + + + + + + 2 4 2 4 2 2 2 ) 4 104 768 26 192 26 26 4(192) 32; 5.657 2 = = + + = + = = = Question #7 Key: A 2 2 2 2 2 2 2 1 4 1 2 5 2 2 2 2 2 4 4 ( | ) ; ( | ) 3 9 2 9 1 8 (2/3) ( ) (2/3) 4 8/15 (1/18) ( ) (1/18) 4 1/ 27 (2/3) ( ) (4/9) 4/ 6 (4/5) 8/ 675 1/ 27 1 25/8; 8/ 675 1 25/8 x x E X x dx Var X x dx E d EVPV v E d VHM a Var k Z = = = = = = = = = = = = = = = = = = = = + 8/33 Estimate is (8/33)(0.1) (25/33)(8/15) 0.428. + = Question #8 Key: D From the Poisson(4) distribution the probabilities at 0, 1, and 2 are 0.0183, 0.0733, and 0.1463....
View Full Document

Page1 / 12

Fall_2005_Exam_C_solutions - FALL 2005 EXAM C SOLUTIONS...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online