28
Lecfurt 22.. - Po 'I VI + E S+1 yYl a To clUj we. siv.-t CV>cr1er r; OVId LV" ,-1- -I+e.. s-fc:.+tS -hcspo,rf bf Co\Jr<) e. 4 - SOv.".,I 1"" - , YVe.., I -l e c.. +u-l' t . '10 ( K SOW}' - It Qccur-S W0 ktA-<;l<.J cllsJvrlh,*kV\ Q)( t,1r -+t-<' vel&. t. . of ct- lVi -k-G+ We- hcJ rev I Crl-tte) ! I . llhe- E , , i I ! ____ -l i . :- 1 i

22.. Po VI ES+1 a ~.~ yYl - Department of …tjp/Stat400 Lecture 22 6.1 Point Est.pdffc/lrc/IV~~ e o.-d l+ )( j5 ~ "vt{(It VJl, v S \,J

  • Upload
    vanthu

  • View
    212

  • Download
    0

Embed Size (px)

Citation preview

Lecfurt 22.. ­Po 'I VI + E S+1 yYl a ~.~

To clUj we. siv.-t CV>cr1er r; OVId LV" ~ ,-1- -I+e.. s-fc:.+tS -hcspo,rf bf ~ Co\Jr<) e. 4 - SOv.".,I 1"" - ,YVe..,

I

-l e c..+u-l' t . '10 ( K Ofld.o~ SOW}' ~.s) ­

#~+ It ~1VfA~ Qccur-S ~~+ W0 ktA-<;l<.J ~ n~eh,'l(~ cllsJvrlh,*kV\ Q)( ~t t,1r -+t-<' vel&. t. . of ct- f,arc~1er

lVi -k-G+ We- hcJ ~ rev I

~,~ Crl-tte) !I

.

llhe- E ltv~ E>(o~~ , , i I

j~-----""- ! ____-l i . :­

1

i

I _

I -

lJ (0· 7)) ­

B· 0oi\V-<M~lI\ ~v~k~~ ~ ~.?O v-c~ VJ,-n L d~J : S;o

~ I. ? (D .,,, ~ -ft frt-C ~P""'j-R.os. c

l

I \,l.f;?Co , d \J. I

.):.9 e-~ fJ" fA; ~~ f I 6-~

~~ f:.Xe-fr-,{J.» 'J. G "J e;: 13 --------ii~f~6wtvL ~ ~

If i-4- .f·C· r"jV: c-hAVI )(, tJ 31.

. - J I I

0\1 SGrefe Lv e- I.J '{ II WI/I -h rts

r1"'.(2 oS rX (x I e) +0 (>~r karr'll

i{k+ ,f- 4~5 14. k~wV\(}11' Vir<

fc/lrc/IV~~ e o.-d l+ )( j5

~"vt{(It VJl,v S \,J<:' V l II \V l( l+t d~ ,Jf ~fX(xleJ OjOl~[~

fA')-- tAu-JI'Q 1k ¥~u o~ 8- ,

I~rv~-t'~~~ e. IS .flY/cd v ••J.w-:> r+ IS6 .III

Jvd Jkrf \.VC: ~It-'+ l~\oJ J. 13~ LV e e v-C c- lit:) w-t'J +> if!.n:' lr,~

t. cleo k-hu #\5 W 1# e It I.J ..... Lv­w-c dor + ko--....t)~ +I J fc.-, r~ (~t (J +­

1 __ 1 _, ~ j ~ k Xu ~ "f_ v,,"" .II---\."\ \11 11'\ •

\\]ow rVfl-~I!~ h<Ff-«CV\O~1v-(>1 uw 4W'<­

S a vY--r~ Xl JX"J--'/~~ ~w c 11-<Jt kl 1 X w~ye ~ ~ \net: 'vi', I\'tJ dt ~tr 1 k> \; -1uJ'" U

kMuJ't\ . m e,+ ~ 0'" Ii .. \r~w ll'\

Y<i 'r If\'-\. ~Ie r;vOl" V t!A" l e,; tt VJ e,#

w ,11 G

c ss () ~ X I S Ji S; D~ e k... .

TI~ Idea. crf e<:l H~rt cs+1 vn:- t-i:lV\ 1S

~ Jt"(: ~\) +l~"'"'J v>' c k, .. J G\.a Q

~lA~S5 ~v- e L:l/e$+,~c+I"J6\A) I f\ -kifWJ of X I J )(l-) . # Xt'I ... '. . / rJ

, .

\.J ­So ik hiJ f V\) bL~

ll~< Ma ,~TVbble'M (VojV( Vf#-fl.U.) 5 . '

Whet -fv~\J~~ 1., (XI) X?T~lX.,) of +k 1~S'xi) J ~ir -'J xVI '''' ~

S 0 ~ r ~ .s ~",}..l tv- c . r1(: k +0 ~_d' 1Vr-~ k

e ~?

Ve+11I' I ~It'\

AII ~ Iv tc-tw"l +.r po h ()I'l/'X?-J:? x ••J Jove­

cJ-{)(.} fc- '~ e s+1 w-ck e WI 11 , t.u.

C< ((P J. ' (.) €II . e J, +I "",,('<t1l1F ~ II'" Q ~

-A S -Flrs+ot-t" ~lJ"'+C;SL;:.,--;0,

r '

.!f,;J' h ',k>'Y-d-~: ~VW~~Olorr~ X"r7X2-)~ -[N,:, 'v~ ~~"C ,:,:', ",."..... ',' ,0<)

h (li'lI>(.-F , ~.,....) ::: &- . , .'. t

11,:51$ b~~,\;d':J wo 1Ve.~ kt s ~ ·SQ~e...t+q<'-j el.K..

611k Ma~ ~lN~Le~ (s~~!¥~~t-

'l*5!II ...'"' .... lIO.;eiillil'lll!'~S" l",.lI;QoA ...

I

~eI K-Et-e -CAl ~re0>' · "\ . ....r_~_~

GIve ~ \) e,,-h+c+tv~ ,(// --k.vt~ I .

~ ck_C-{~ w~+f"v' OYle~s+I~f..,¥"-I

1 lrl'W.=="f)(IL)(<-J--yJ~ £..-1 8 IS ht+k~

+hq;~i ~ e::.,p~NJ-~,.;. hL[)(UX'-I~'/XVJ.

·Tk 0 t,dVc-vrV~tQl'\ !) ~\i .~ ~ . 't11w)

Is .>~-,Il;~+ vje~l.

2~ Ol'<lw ~ ~k. ~rJA Uu.­

_u~ v..re If-<LHJ +0 o ....s,~ I

rl/1-~;Jof;Vf-~j ~~ )(.)1 "'" _ . odtev<VtrJs . 30 lc-k~eJ>re- . .' .'

(j i'\ (/ G~1'I1 · s ~t... /7' ~f~ ,,, '~ ~ ore"'.Lt.,..,.."',

- -

7. " :. .

, '-----~ X ')( >< , . "'; ,,' '\;t)", ,7..,.1- - / "" I i

, i

',N() v.) , OUY' -f\i~~~'" h i~llt~l'"t.l~ ~ Q v-,;... ~ V C lI"LC> ~ ~ (s ~+u·hc) ..

I ' ' - ­

;Qx~SC¥\ ,k ... ~ Co>~rri..s rO~ J I~::>

Q~+l.,~<ffulr sr:le-hs-tt.c will cA'_-fe..-. he.. /,,1-;' "", I ~-

'~a~d-td . /t9' .. "

I .

8.I ' !

It- lVc. 0c.v-e Crl ce~ 1 SCI+-f ~ ...

+k~ ..f-e.t Ylvw. ~~ h ('><71) /(~J'.I x-",y i

,<; ~ H~J 1-4. ~~Sl""lrrcf V~ lve.

0+. -+e-c 'eS+'Wc~Jr s1z+Lj·Jt~

.. W:;:· ~ ()({) :(Z-) '.'J X'V\) ft-t."'09'

~ 0 1V--(1 &. ';Q( 1>7;..) "'I' X....· . UI' f' V 1u ,..<' fr-~ .. . ~ .

I +- -to~ IJ. (),(~ ~-kJ f9. .

t<cwcv-k Jh ,erJt~J-J~ J4.+0 ~ t S~\)lJ ~A dU-.lkJ 8 ~d 1~ oh ~ev<lfJ velu c .~

.1

b\r~ 11" ,,~ 1f1(C~ I {Of-,.{ ( b. 1- t ~ t.c a I) . L_ L --' re ~V'~H,\ .. ClJItJ/:r}eK+'

- ' ~ ..

I

I

fS . YYl (/, xi"" f "Z-- c d ­

1(') ..

! I ,

i

y n blcJrd E.J+/~ ~-futr.r I')_:9. ".', . . . ,-i r

.l10W\ j}\l~lw- ( ~;t¥!::;',,)

b"ld. 0'" eS+,w~r :;' h (~ ! - x)_ I ' ' tv.l J/ . I - '"

, I

,', so#d-· ~ ext, ('c+rci VC ItA e.

,s.-(wJ '0+ ~'e~l~~~r

Sck+{.)4t~ 'W Scf:hsA~J

,t=\++1 rsf '31oM.ce- ~";;xJ ~J'~'+ le. II k. VvtN ck l!.PJu¥ 10 a c j,.,:;cve..

,-ft~' (iii~) b,,~ 1~ ~c+ ,1+ fJ

,SVVrrIJl"311' e.--)jh ccl,qrvc. ­

. LL ~._ -nA_~ ere,t¢' ''J",cT .' lllU e..OJ'j · (~ "­

'~J1.AI ~" ~dhs~ (}(\>c) ,

~0 \,lff',W',14 'HICJ.J;.;y~ C.n :/wto...

12 · .. I

L~-J- J ~.. Ivee_.J 4-,,..,. r> J..rr -:.tJ»~1 , .J~ . ~,J "sqt.,··] ~,J Tle,J

~+ .re 1lsfj. (jeo';;;; a ho,~(?:;, ..

,i I

De.*'t..,,~V\ i\V\ est-I~ ciov- .dc--hsllc

I I

W~ '" (Xu X'~1 --/~) i> 0'" i

()" ttcrJ l-esJ, 1'r~Y' 'of tu. ,

l!Nvtlb~"r~ro~~"" e tP­

~~- Erw)~ e~ " r 1

L VI+U.,.f-IVC S ('~) ~"Q~ t~IS. .1 i .

b\J\,f-' we c.c~ ~ir..t.c -tits ~t;{ free'Jc

N!avu.ws. iiM~J' '1'\, r/l\)~c''/I~e,

C~kd"vJ. "",.....r?J} \rctA~-J .. -'(.. . ." .j ;) :

t-)(G( n,~)es "af UJII'b,~s~J_EsfJ"H~1'j "IS"

n~ ~O&+ I~f~~t eS+I~~~~_

t~+s -h~ QVW~ {p~k c+ ,.,. ,.''\.

Pnlo ~j I c"J ~ (f"Su I o.oJ 2J

Fo ci - rhv-"" Q., RcrrlfJ vII IYCI' J.o VOv'"lobl. )('\.1 8;~ (IJp)

(.vc: ~-~~ E- (Xl : F" o"J ~~l:~~ ~~:~c~r~Jv~~~

I Er'X) =,\.

R-~rlvJlJ' ~ IJ' c ~j . /7 Sr~t~ dc>lh--i-4", ~ *!J ~

VrLc~4ur, w ~+ ~ V"~Vl:Jl Vj

cAl0tvf~v~" ~.

~e-c)IfM ( -.n e... sClI'Y-y/e l'11 e.-e.A )( I S a",

U vd? I oJCd es+' tM ",1uV-- of ~

fc:> fIA \ck.... Yrtect" r 3 +-h~+- 105

.1 E(X)~I

11-u~~ -rk rwuf I~ s~ slMr4. ~ cA..(>~l/t{~:) S""11 ~. ~. c C'-' w.. ~\?... ~..--ew- \J; _ So 1VIr--~ r +?: ,,+ .

E(X) =E ( X,l"±,~_+.! ?) )

" V\'­/\

. / , .

• >

. \ . \ i (

- .". ,", --.. . , 'f

I==- ...LVI ( E, ( )( fJ +- -+EC)(~ /8 . I I

'v+ E(X,) = E(X'~J =.- - ~ Ef; ~)~t1!

• .!

, I I - \/ \ - . .b ('iCc use a 1 +k- A.." s c ye..

! " • i .,

S Gwrbs fvo~ 'it}, ~f ~ 1c~~ Ja '.

~ ~1C1ve-- ~I Iso~ ~S1v-~b~~V) O\~ # l'U)f It-- lc ~r"\ r-o ,'

E (X )-:- J(I\ Cr-rr +-- +r) i ---../--..-..J i~

'0

- (;;v- iI--e.. rh~~~ of- es-hfrJ~I. I / 9 P \~ Bl",Cl j p)we... JI-Ove.J

i II .

x:::... h v ~ 6~I")oF-- .ob J.I&y IF( <i :s t,C-NJ'I1'.). . ./

S'VY? ~ e/c;;~'\~. C:I+ X';J)vl.-j--/~, , /

lJ et~ I' ~V-- Of S-o

Ih v.s. ~-X, is: ~ IIClOm l'MJ"JU!t-V\~if~Mct"5 +k rt:,~k .~ w- ~~,." ~-f" o_J'~V'\,d

I

AY1Exa~pl~ k1/htyt; ~ 20

1(~mroM Se~It"E... s+'jHlct~rl.s. ElQt4'd, I I" ...

0)'[ eXGWlrl.e o+-4t.~l:" fh. / - I ­

1trJ· . . + r L

1 '»)\_I a" J£,vY\ Ott ; u~~ j e ." It-J "_"j11~;r ­

. (i" rer---,' ~ t~ .- ~

I. - 'I

R~()~_ Ve.'~ Sf~,_)otr pw LJ ~ o C cuvJ l~ Exc.... r~ 3 - eS+f"","~ ..

f7 I 8· 1_D III c~orl"J (; Y~d-U~ rl\l"" ~

~ I ­- \

I

- )

22

-eS+/~e~... IW=~~X' (~I)Prz-r-;; ~..)

l.s . 'b ·10.1e. cL ..

E(Y1C)O()(IJ .. J X'~. )) <' [3.: =1= ­

I I

A~oz/'"j(~ }rf fj~>Ai k rOjt 250 p£A.l~ ~ '3 ~ ca 'I ~ tv.'II r~(. _~,~.~ ~~ ~ ~vJ_~ ..!Y' v cJ,... rf- .. ~~~ £.~~~: .. W-C~ •.-nCA)VC(p\' . .

E (Mox> (X, )Yi) "JX-l".!J ~ n 13 . . ., .. Y\.41

- .

r'1U'1IV11uV11 VanollQ. UrJ;IQHc1 23 .E.S.+/~c-h ....s'

We, have Ise€'n+h c+ X-ond )(1 Q~ Vl'\biQsd es.fII"M~<1odO+-~

po \' <A \ c-k. '" _ ~CI\ • C~ "" t1'-O 11 ~ (J.,.,<Ie...

\ ~\\ . _II t. ~V-,,· 't -t. ­

~ l..S V S 11'~:r 1'\ r;s ." IV A.#'

ltv k+ ~ <Z--t-tc,.,.chC<;olcv,-\evc<:\V\ ­

~erc-k.J --\-kwt, ... W(?;· kcve...

~-. .... '\.. ----- - r\' '2-_ pal'" t9~""X· ... -. . ll-u-~ , ~VC V-cvtO~C~

V(x)~~· ~ 0- ­Vex) IJ ~ Wf.!~clfw~ V(X,J. ·

,LVe- w"//fe~'/~W. w.lj. -Htu :24­IS. ~ (.J ~ c:l . . Pin-+ we. s -k k

] ~ .Pr,~c~/e ~-!- M.(w~.!.·r:-~_ \La Y I ~1I ~ Uh b1 e-JI' d t::sflJ1'14 ¢~i1

A ~Q~~c)l eM-/ f')\ <7' +o~ rl- e-M are UI'l b'Gl'tc1 ..) ck<JoJ-e.. ClK~

-I-t e,f h~~J Y>1 i '" i·~ fJ H/t V c:. r'; 0' A (" <2.... •

771t. ~J ... I +l~ ~ s +1 Yl' c~"; ·,s

cc tCe c1 () Y}1 j r ,~ WI v 14"\ VO V l elf <::...Q,....-

Un /J/CJtJ eJ+II""'cJ.vr.;; NVUf;.

.~5.· f ­

-

a Y'Yl; Yl i Y7' v YI1 V" Y l 0 44 ~--(!..,.X IS

U n bI (,I Je d es +,#1c~r'" .-hv-+k . i

f¥oh/~J d I

1_ .Es +,;¥ccfl'.j F 14 B,II' (I/f)

d- Ed'/VIah"'j l' ~,,--N(r/<s?j .1 ­

~Wir3 Ist+ ~ ,,~.J .. '. L

. /411 11 ' J1A/~ .fA.- -! va v { 0 I" <:::L ?

\ "".

(::\ .' .' ,dGSu fto+ e~: h (Xh x.!.) <-~;y;) is a..,h e $ +U'''''--<Z +-., y s-1217sJ,c -- t{;I/'

011 1/011 ~W;' Jtcnrc lVte iev- &.

·' ·.4 e ~.t1:"f ,', ~~ ZO"D f

The-~<z--c"'l sruorc J eyyOV'

M S E (13) of -1-4. ~:5+IcA-~+a~

~ __ I~ k-h«J ~ . . -. IA . .. (f~ e~) 2.--- --

Ms E (/e)::: E (8­ j

I

rSQ : MSE (§) 15 ~ ;)7I'

,I SQuared e,yor (r(v :.J fj)""..".",r2-

J

".1 . ,'1 1'\1) -./'X'J - ", .'­r I .

~ {' .1& .e c;.+IIMc'";,

-Ie o-f- \7,/j'.' ~~l 1 (....c.'"\"'~J--­,,r-

Ll::.,.:: .. yo ).n • L J ~ ,

---'

. Cf (r(7yt;jQ.d Olftir ~tJ '></;) x~)"., ~'.

o hVUlvS 6:J "V.~ fAJ a",,+ . ..J.o WI ~fI\ ,,,,,,, I'-t. .

-/J.. u s;.~ v 0 rt J erl'Ov-• /-/erc t.J 1te­

r/~f

Th (VZ\ r:IV' I.if .1! IS ulJ1 h,oSf.J ~

-H SEfe)==Vr(J)

. - .. ..' 'I'·

R'J ~ rle/'ft f~'" ~f! 'fits t.:ri "'~''>, . l;((j ') . r::::J

"'+. .' I

.

l-k,r:c IS o,,! i~rr--k.-}- cle.fl""(~'" ~JtJ . a .1r.rJ ,.., ~~. ..

Vef,~; rlt.,;¥t ( -k-4 l~<2- 23?)

~. sAt,"'cUvdevnu 6f f4 eJfI ~J.(/"'

..6' .). f)~~J.· ~(i" Ij {Vf§)··· 7-+lf~JA- J~vh:lsq {J 1"'1c

-fvW?} ,S ~ fCJQ ~3 g ­