410Pr3ans - (; I 04:. 49‘ ek n "\ Cx-y V 0‘3 U @(x...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

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

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

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

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (; I 04:. 49‘ ek n "\ Cx-y V 0‘3 U @(x 3%\:W igx‘ fl,(©<x <93 \?\ f>\ e M A Q~K 22:... (WXX &(maxx\<e\fi(mmx >03 Mk (—1" 9 But) Pacfimhko—n MOM) Y :MM X \s Sui—haw g“, g 8 I / CL“ 0 9‘ CL+\ 0k+\ 6» ‘ CA V53 bum/N) E P EDA; “kg 01-14 P _ I _ V «P _ :76:‘f::132 LKZ'Q(K\:8‘ a g CS c. stsw Q’s'kmkkw—r cg 9. B 7. am E(X1)'-S’X1*2\1:XOL4M— 0‘9 o . "’- ’1. eke/L Vw()(\: 0&9 ~(0‘8) C/LT ) J? (“2-— E(><\\ 3% NCO) VGA—(x33, ’ ~—- «9 b 1 V. 07 (X w -K+\\ —-—J>/\/(c:) 3‘9 \ (a+—z)(q+‘\1 ' 588%: 0L~H Y c; 04><\<e L‘ CL. '4 «4 Wm K 04 1,4 M°\x'.50 “mm 4 >s e (:9 t a "\ 04k“ 49 MW)“ ‘9 Lg): ave. PQWKX; >/ 9 +%\ :0 t» ': ()(waXQESvL—B 2PM)“; (9"<\ =[$X(9~$31n a Fxbc}: 2:; ) o<x <La\ .. “ck =2 P(\\%—e\>,<é\ -— (e “} -~—-—» 0 9 kévoo S «01 9;?— 4k 9 r\ P i\ “v e) A 8) M 9 is 6‘. canssgw ggk‘WAD—r‘ 9. E(‘5)=E w- ’ (M : ~ M (a X3“ ‘2:— (X3: f/Ax v 0\+\ 0.9 c» &+\ vg’ mai‘ I" ~ " ‘ 5’ 6 ts a,“ WAL‘Cqu QJ§{‘\M0JL°~(‘ 94% ‘~ : 0L+I~ «1— l ‘- VMHBX Vw(.a_\_ X)‘ (01;) Vor(§)=(0\+\) 6‘ fix _ (6L~-H\L (197' e"- ‘ Km“ \ as. L ~— N (K+L) (@443 In W “(KJfiLS MSE(é’) : (Lumen)? + vww) : O + Rik \ 8L -— N ' C a ) O c. ‘JL 9. CAM‘\ ‘1. QWA*XA : a-V‘ an ) 0431 (.9 ~ e 6 xw’w‘ M ‘ (1M8 /\ ‘ P‘ ‘ t X an a v - ~ t: (MK )(‘\ 96‘” O A §dn8 ‘6 b\€\$(€ : -9 t B K ' L 9 Al V“ b(@ 3: YXL CA“ X A/x: A CLM v e OLH‘fZ— VMé‘ ~ 0‘“ at (M931 m QL ’ W _ 3:. W M+L W+\ («14+L) (Am+\)l ~ Ms :(éx : OM; (83$ + Vw(é‘>3 9L 6th 91‘ C I + (ah+\\ L‘A“+l)(0\h+m w W @m+L)(‘«M+‘) L\ Fer 203$ h Mgaé‘X: “28 <~ E9 (am+z,)(am+u) M0~(0\+L) :MSG(’§) \s c\ 9—S‘KW (hm #1312331 ) 04143 X“ v C; "\ CK~\ Ca 96k \ an“ E: X \ OK £(x3aX: (ck—\X QMX +5“ 6k —uQ/n9‘3i ‘33 P e PX %EXQ~\M :1 Q9 0 K+\ x: -— “— X 3C+\ "> Ck? - Q’K :3 \JL) GAE LUV) '-— P p. e X Q t()(\: a" K+\ (OLX— L ~ - \s “adv a 06 avg; WW oi 9 &+\ -9 as V A, _ P OLE Q :— (K ~———> ’ “ a,“ _ a “k 63> and) v 9 as w ‘ L \FA _ k8 D UL 0 a9 “+‘\ / Comm/3 (own-LB” C/O-«évr/Lbr Q(7(\ : "L gar—x, W "‘ ’V °<X(K)’a 1 ‘A :f\\=a\ / 6 (463-1 ‘_ " me 1 C3 (9~-x.)’— X a“ \ : (0‘23 710 (La WM“ H ’3) e1) ~ H ®(G~’C\\—% M<O (“H3 (x91 ) L ’ “M a (flu-7,) (outfit 72> ~ “0"th xv 0 5:93:23} ) Og—QP’L i 0‘ CS “rm, N< 6\) CL(0¥+\3L) V‘ (Gk—+1) 2’} 1 a is“ Xa—\~ ah . :’/\ 9R \ "‘ “8am 30k~‘ Q. A i A“ =0 :7; a: V\ M 3 h a nue~ ZLX; -3; tun) G :\r»;X(eQ:W)::\—.(%§;7)“ : \vz—o‘w W>O A K 0;: 47: W (5%“ WI...ij ——~ P a» CLT) \Vw (W'fiw') 3% AND) €333 fka—«Aafi yak/(o) {:13 Comsrw 060’“:le- ‘”“ a<®322 i‘ 7 m\:a\, 9 M '3 x3 L, @053) : 36 S:%‘*‘ M : 0~ 9 O a“ can; “)3. %(o€) 2 gm :5 W‘kw we ae‘ B'a-‘C (1+3 /\ 9.. ‘ 01651: '7atfima_»fi9§3:3aa taxi“ our“: /\ a \8 N53? 4, Lo-hsisk/VVJC QsKMM‘w/f‘ a; 0‘ 33 $\\AUL wwwl/ 1w” Wt {Zak foowMHcJL wd’k MM .3. 0x ) ly\ . X V\ ’ZuA= * I“ L e) gw has 0. CKMW AXSRLJVQH WVH—x d\:: h a“;( r) l A“ 0‘. k) ‘14 \< 1w) G: a Owl/“max (eL, 2.. \‘oL_ “5'7 7. ~é; Ln ‘ J \ 742(th K ( 5 fi X‘. ) _h7 v ‘3 0‘ "°L)"000/c 132433 'LQLLg—‘B \ {MWVG‘Q @04- a. , ‘ . Qh\ g“ I 04x48: 1 3; F55 (*3 Z ) 06.x <6 0‘0 Rub“: "' (\*‘:x(*fl ’ Va . v- FV (v):()(v\ L(\éfl‘r) “F‘fiLw/q : \' (\- FKL§a\\ r k h :\"(\*:€r°‘3 , Ocfir<mV¢efi _’\3""~“/ck LCM FVP‘VU) ’ \E Q g ) “I've ham CD? o£ QAM km :S‘ wiry/e“ FV‘v)‘:{—' 9’ J ’U‘>o ‘33 CW“ 1: ($K(z))m Fww‘h’”) ’— V\(e'\(y\\ éwx ': PLYV‘ ~>/ 85%) .: \'— ;,L(mk9“%3 : \.__ (Fx(e~i\\n ' 6L O<w<ne 1 PWva) : k“ 9/ ) W50 CID? OQ wakfia MSWR‘JNQH es -Qw/ PW e e 3 wiH‘ PHD—QM a: . b) d) fX(x)=fX(X;3)= 2 , —1<X<1, 1 2 3 1+Gx x 9x = E X = x- dx = “+— u ( ) j 2 [ 4 6 ] 3 N - — 0 E(6)=E(3X)=3E(X)=3M=3—3- =6. :> 6 an unbiased estimator for 9. _ P e ByWLLN, X a w? P P X” —-> X, a=const :> aXn —-> aX ~ _ P :> 6 = 3 X a 31.; = 6. :> g an consistent estimator for 6. l 3 4 E(X2) = sz-Hexdx = = L+9—?—C—— _1 2 6 8 2 _ 2 0‘2 = Var(X) = 1— 9 = 3 6 3 3 9 D ByCLT, fl (i—u) —> N(0,c52). :'_> 2) 2) D «Pn— (3'i—3-u) —> N(O, 32-62). fi(6~e)3N(0, 3—92). For large 71, ~ 6~N 1 —1 l 3 . f(x)=—2—-—%-x 0<x<e 9>0, e 92 00 e 2 2 x2 2 M) = Jx-f(x)dx= yx-[—__x]dx= .___ —oo 0 9 92 9 3 — N N __ 71 X=9-. 9:3.X=3._1_.2Xi 3 n i=1 fix): 2x 6<x<1 0<e<1, 1—62 Likelihood function: n 2X 1 n L<e>=H[ -n<2x >, i=1 1—92 (1_62)n 1:1 I L(6)= : Therefore, A 9 =1’l’lil’lXZ'. min XI 1 b) d) 2(1—x) 0<x<1 0 otherwise I f<x>={ X" =gzi=1xi§ _ P ByWLLN, Xn=l2?_1Xi —>H=E(X1)=%. n _ Tn=l(X12+X%+...+X,21); n _1 2 2 2 P 2 W1 ByWLLN; Tn”— X1+X2+...+Xn —)E(X1)~g, n - 1 n=‘/—7;(Xn ‘3), From part (0), Since g(x) = x2 is continuous, g(fi(§n—%j] =n(in—l)2 g[-1——N(0,1)]2=% x20). 3 m Wn:fi[i% __ D Frompart(c), fi£Xn—%) —>N(O,-1—1§). . 2 . . . I 1 2 Since g(x) =x IS differentlable and g )= E ¢ 0, 3 fi[g(in)-g(ljj=fi[i%—éj3N(0,(%]2x1%)=N(0,é). 8. a b) 9 2 31—6, P(Xi=3)=—l— , 6>0. 3+6 1 .9(#of1's).2(#of2’s).1(#of3's). (3+9)” f(xl;9)f(xz;9) ---f(xn;9) = 2 Y = (# of 1’s) is a sufficient statistic for 9. E(X)=1>< e +2>< 2 +3>< 1 =91? 3+6 3+6 3+6 3+6 n _ N _ ~_ ~ i'le =x= 6+: 3x+6x=6+7. ’1 i=1 3+6 3 '5: x——1 L(e): 1 .e(#of1's)_2(#of2's)_1(#of3's). (3+e)” 1n L(6) = ~nln(3+6)+(#of 1's)1n(6)+(#of 2's)1n(2)+(#of 3's)ln(1). 3-(#of1's) n (#ofl's) n—(#of1's)l (lnL(6))'= "375+ 9 =0 :> 6= ...
View Full Document

This note was uploaded on 04/15/2010 for the course STAT 410 taught by Professor Monrad during the Fall '08 term at University of Illinois, Urbana Champaign.

Page1 / 15

410Pr3ans - (; I 04:. 49‘ ek n "\ Cx-y V 0‘3 U @(x...

This preview shows document pages 1 - 15. Sign up to view the full document.

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