solutions3

# solutions3 - X i pyg up' ip (1) } z s { z i b~|Uwiyuvkyg }...

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Unformatted text preview: X i pyg up' ip (1) } z s { z i b~|Uwiyuvkyg } z s p { z ab~|thy P 1 i 2vkyg i s i s p ip uvTxUwvuvrt'srpq' s and are independent then 12PCD9 8 C o D\$i H C V9hI CDe e i `9lHk e ie c 8 \$i i j m m nC g R e 57 m P'U d q i g e 555 d` "u C i vph# j ic hef 5 6 g 8 4555 H@C i c@ P\$`PC C i H@ i DebEC eGC c H C yebH yGC D9e 8 i@C vFPrd 3rwvD BPx3rwvutU3rph# q i @ C q i s q i g 57 555 5 4555 (b) , , and , . So 1c d fe9 C c H H W @ H R A @ C 9"ba`Y3XVFVUTSQFPI H 9"GC A@ FEC CD9" 8 A@ B 8 9 8 6 3# 1 ) # % # 20\$('&\$"! Chapter 1, Problem 1. Homework 3: Solutions for , On the other hand, suppose that (1) holds. Then (b) The next one is true by definition. Chapter 3, Problem 5. If Chapter 3, Problem 4. (a) 1 E E , correspond to the following zones for : . The three "zones" Y X 8 % 1 '` i i Vvk'D tPQ pT and let denote p'`Vxp' i D i ip 8 \$ V U W V P s the range of . Then i ip Qxpq' R P 2Sp Q . U # s khD 8 12b}yzw U'wi{yzy~ G uBABykI I{ !s s D 8 } z s 6 z A } z s p 6 z EB~|tPI{ !s @ z s D p { z 8 !} bU'Hhyy G . Then, F } z i D 7 yphECi { z d 8 7 9 6 { } { C 3 1 # V5 xv4\$V 2v\$V ' C C V0 xrh\$V)# ' (`% I C V& x V%nx C C qV\$ sks IXq`\$ I Vd kwwV C C s d V#d s !" !s `dtpy d s d VD # !V(nC . Thus, d d sp \$t9 s and hence, Chapter 3, Problem 7. Note that and hence and are independent. . Therefore, C u and Thus, Chapter 3, Problem 12. Let Chapter 3, Problem 10. Fix . is independent of and denote the range of 2 Y X # uvkyg i A B } and let if and only if and and for 8 d s C Ep 8 3@ USs 7 T R i i g Tph# 1 i j p ) # g rqvk ) !uves krvekrvky# i # i # i # i s i g C D 8 s Chapter 3, Problem 15. Note that and hence . . Now, 8 2 H 3 2 u`3r0 1 ' "! "! C 2 Db 2 2 Q P ' "! E 7 @ BA @ 87 C AI 1H )G '9 )' A 7@ @ 7 2 FE D' CBA '9 )8' 2 6 s R j "! ' ' t' g u53q q 2 4 2 ' s h' 3q R 2 0 a`3r1# 3 3 1 ' " ) 1 " '` ' # ) 3 ( ) ! C i i up i u' i % % & " \$ ) ! C ' i upg ) ! C i i yupe srpe etp 8 has range s i g ksrpy# s Y 8 X V U % ip p' (2) i rvk'D 8 0 Vx V U Qxp'D i i Y 8 X phD i E Y X 8 0 P i uvkyg So 1 i i &Vvk'D `x `x C Also, Thus, So Differentiate to get by (2). Chapter 3, Problem 14. Chapter 3, Problem 13. for . 3 . And, 3 { z sp uSyst9seui . Then . For ui # Now let { C TD PCXp E2Pp 8 Pp 8 p 8 p C 8 s@ v\$ W 1 C v&nrV Cp C p Cp p q` iX`xPp 8 `IP2 8 vQ 1 R C v yrV 3 { C a 8 @ ' R C { z s p 2(VWI 29btyqyV\$DeyV# { l\$hC C p C C p C p P`R QPp P`IP2VIp 8 C DD0hC s . Then \$# x y C lT 8 T T #uR # # 3uq\$xn ) kyy # C Pp 8 7 T 3@ UR " i ) Tv # For and since Then ' 3 C { sp C V&nI 2y@ z y V\$uVQ)# Thus, 8 1C D3 8 8 hC C R C V triangle with corners and 1 C3 ui and that , let Chapter 3, Problem 20. Let Let be the triangle with corners at . , let for every where and note that be the triangle with corners at 4 . So, . Then, . Then . For , let which means be the . 8 1 c 18 1 Y A iR Y A C H H A A d HY D YR Y D H u!YS s R d a d (e) (d) .37 ui # C d D For , let 3 C { sp nxSy@ z bt9yui C P`IP2 8 `xE2 8 p 8 @Cp Cp p Cp { and 1 C ' 3 ui So, 1C o `DD ' C D 8 3 @ vPC 3 PC @ ui This is equal to Chapter 3, Problem 18. (c) 9.58 (b) .89 (a) .84 be the triangle with corners when . 5 . Then ...
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## This note was uploaded on 05/25/2008 for the course STAT 36-625 taught by Professor Larrywasserman during the Fall '02 term at Carnegie Mellon.

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