i vremillson/teaching/stat400/stat400lectur… · i vre ... l. e
TRANSCRIPT
Le c..+wre. 7 li #ji
1m ,,""'$4'
~ Ev.~_.&S.·Is;. DJ SCf'ete..~ .... ~.-_ .... ,"""""&
Q~~"", VQY'\ Q bItS .(- gt~'C)~~\Q.l I
I
i
2 - \'--\ ;:)vre I"'" 5eo(;) 'M <:.tv \C. .
3~· Ge Q ...~ tt ~,t"Y~' ~
4-. N~ ~~+wlt. 15 lI''1 CH')"''' let \
5 - ~C> ~I ssoY"\ .
E eYI"'- ~_'C kj i + lITO .rl +k H 0 ~do() v. ·h"o- b Q. s "e:
p ('0 bo 'hI L~ dlSiYi bo.-hC)f'\s'\ ~ CAVe.. Six dts+V,bv.~Jls . I dId ~.o+ lls+ -tk. 13e.... l"lo .... Ui oIls-fr,h":h.o,, ahov<Z.
6eC" a vse. rI- 1,$ fuo .s IWtp l.<..
Iv" -t~\I S 1(' c-h,. ore- IAIe IJ ; I) d.o
J. O"d ~ 1 0 b<>11C
. / he _B"itOr>7iC.).
D,s+r;Io~~vt ~ "
S~ Pfost?.. We.. hfffle a 8erl10 .. lIt
eXrey ; vnr:~+ IA./;-/t. ~(S) ~ F;:J for e~a fYI! I.e.-.J Q W .e fJkfr d 0.);""
41; -/-h Pc 1-1) =:; f' AS" U[(Acj! We.
t u.+ l.::: l-p· i. ' .. -I-Repee! +I.t (;effr l ~(" ,
,\ ('
(-Fltf -/Ie C<l 'VI) . Le. t: ._~ /i
X=-tf J' SLl cccs~rJ' ( #" err j, (' oJJ) ,
We.. VJoy,! 1+0 CdJlJ'tfvfc, ~
fro he ~ (II ~ I cit Sfvl h~ -Ir-o~ of X. NGte. , ~ (. elf1- -I-h :::f ec~ &/ Cek" -=- J /t- Ll c.-fu.re G f 1j flJ 4 c~j ~..
:s :/ / ). Vl~
Als;.o .' -F ~
· PC )(~ 0) ~ ferr· r) =~ ·z·· z~t' ~><.e.) a Itc-/UII'!I i i f,f-li/rt. ~ '-'Q -f Se,; ~ Q.. .JI.-e. 0 l,-k..t,1I'I'tV 0
~ 0 ct f!.f -Itr ec+rJ i ekpey; mf'llI-1sI
are 1/Jdep.rl1:.~ so I .
f((T b" 1)+) 11 (t ... t"")/l~' ~ (ToA k*0
-=1, 1,· 1- ~ t ., ~.r"-_.
NO-k- To"l;~ J'r'-r~~) , .. 2"d. Ufl'-# IL·~ o~ ,~~ r'h-C~IA S~·o
, Rim I ..
p(X-n~:; PcHJ-/-- fJ Jr r t1
. I
NolA./ ~c h cvT -10 vo.,-k I
ry h~1 h .J]( X'=- ,) ? r ''--.. ' I I
A~m~:'5;h.dC',,"~ Jl'l41~~
I/k~v~~ (X=I/)/
c~j lfT~-~-.. -; '. ~
11-/ OK- lvoTe-tv~J,
- =
Wh-j - ~ 11 e ~d. do-tJIII 1l Ao·vc. 10 CoYfte 0-1 Wt ··fJr.s-f ~ss.
<SCI IA. ~c/+ . I
({_ J)~ Hr~'4.T LJ T Hf.,TLJ
•. !," o!u 'T~T····TH
AIJ . of- ~ II e L/f;«* 0'" -f1-.erl)h+ AClA -f4 Sc~ f~beh,/~
Y) 0 YVt-c l'j POf- ,,~, elite!. ~ C7v-(...
yYt C, fr, c / 0J f./kc'/l.. rr vt" _ There a 1-e.
Y1 0 f -f-t, r t't'. .f'"~ !
I !
f:)/ ;', If-II ~)(=I J ::: n fr-
S, m( !fJ.r 0 p(~X'~11-1 j n f A~-: .
(e" ch Cl'-Jci l-I c-.J r c l~vc)
·tf-' rs+ We 'h 0 fc..
/P( H -';.-/ + IT· T ) =- P1L ~~ k. ~~
. 1'\- .l~ k.
Ii01 0jQ'IJ1 -f4- heoc!s do",}! hG'v-e- 10 G.orlte --flrsf - SC)
W-~ i1 ecd fa
( I) C'J 1I #'I + c I / +h IJt' j So ~
Jf>~jkz " I" If c~tf r -fA 01 ~~ k /<1 5 C'~ JfA Vo
Y'.-le '\s. I
(1) )'1 u l~I r1j -H.. t1 11- 4'r b.J1-
~ p k Q H-k.
So how do \..Je S'''llv-e }.
t ~ I ~ k of f~ U; ~.5 VI s ~+ J Vv~~ 'k- H ~ Qt- J 11- Ie. 7:..r
.----- - -- - I I
\
M_Q/tI\ 'Po,,,t OY\r~ J~I.A c:l"'C('J~
\.J k--YC. ~ k I-} S 5~ !j 0 \..l
ha vc I/ta c'~ \c c lvi# ~
T~ - T~J "'f)~ -+0 3~ tA
~ H fN\ 6' I'" "".J )/1- k. sC-Il+s,
So cko~~ 4 k--s: ~
Lv ~ ~ ~ "..1. J~"" s: t.Je,
lev<- ~ ~ck c c.'~ 'C: e ~~. 1:::.
--I-A, "j-f ~- V\ -tt.fV>J-J (Q C~) .'
!
So ;Wel hqve.'~Q-fllv~'kJ-IA~lIoJ~'~5 OL{+/IlI~1A I
1)e+IVI f+(()~,
A d, S CY'<: -h:..ro l
., d.o~<
Vo V I a'~k X IS ;ro,d ~
h ~ ve. b. It Olfof LeI Jrsb·', hv.-ft.cv1
vii ~ po f'fj l'J\ t +e~s Vl C' "J f ( 0 to bIfV \ <; ti' J ><~ IT if'! ri'l.; r) I~X -fc~j lIC~fj 0))) J' ~ j l'l
Ott/
\h~ -k~ v 5(5 x. \iIIS-\c.eJ of l .tr +k l~dcreA' ~+(,:e '~flJ+) VOffe to 4., ~,o ~I.l !.JI)" IJ k .
~ r ,+-\e~
·0r0.s.~ ·hllv"l Ift,
.II
"Sup rH -<- XtV B,VI (n/ fl' ThoVl
E(X;:::VlP o~J vex) =~ ft.. So 0-= s-k1dord d01<IQ~" 1~ . Remork
1I i
'-..,$... ' I !
[lb& ~Y-m~1 ~ ~r E.(X)tS 1\ • , ih, fA + .\A ()u. jI)f. (.n, ~~.. e, ~"{). " ('I. l ' ~~r M't'~ .VV J J .'.~" ( v ..../-\
~Ov' -toJ5 a l-fa III' '-<) 11'\ I00 -h~
-flv E(X·_) t e x r(' ckd V\ u"'"' 1. c.r
6+- 'hI' ~l.~ )h P =- (l 0 0 )(i ') -:::: 5 0
HovJcvtv t.f ~.~ '4055" rl- 5/ -H Vk.3
~ E. (X"):= 31 -, rw+ w~d ~~ .... ~rct+ ~ ~ ,
US" Y\:3 +1t~ b,~o~ la 1:-tc hIIS
1\
-I~ b~~ A1 '1\1 --H-e- -fe).c+
p.<3 b <: 4- - fa 10 b ,
+<1 ),IA lc-k j' -#-e..
c-J.f B(xJ Yl.Jf) fur , h'" SJ 10.1 15) U )2 5" 0 1.. do re ill c fr c:i
've tw.s ~ f'
Ex(} YY1.flt 3·3') b
SlAp PbS0 ~ cd :10 70 o-f' (1 11 ~fi(j of a roy--h C<A lor --kx+ ho~k ~" a (€'f'-f.cA IV\ 10 ! 1\ J1ftj s+teII ::r/~ -Je?'! ~
k+. X de1/101e- * )'I v".. ~ 01/"' a y)U)¥t~ I
IS rO Vl ck1l'-,~ Sf_~('C~J ~r{r -U·,,1· fa I f -l~ to -k -;-f . F- t ..d- I
'11) /' 4 -< X" L """''''''''7"'''')'· I {" -' -". " " I
I
~..~ .. 3 ~ S ~ .
So ItA +IQlII " /2
X,-v 8/h (J5J .. ;D. We .. 1):.("..W 0 " ,+ f'i' Co ~ "p":, -k_ f ..•~\/~:_,,~-"..-/-"~Z"'r·. '~."I
vrr"j -+t~ \ L,~ ~ IrCj~ 6~4-1.
~. :hovJ ,Jo we- W~/-tC- Pd+~ X~7)•
in -krWtr of -1eYI4.r 01=' -tl-t; 1oV'Wl ,p(X~aJ ,
..
RYl&,l,/w c#) r (+=)( ~ 7):= r(x~7)-fcxsV
So Ft 4-~Xs7)~ J3(~·15.J.2)-B(3j 1~·2) ~~ ~~G ;
~. ' CfCf , - .. (,lfJ?
=: • 3c:r8
UI' "r'lt S "c! .: 1 ThIs ~ k~,~ r
VSI"'5 C(J ~ f" *"'s O<Ad sfd/sf! t;D( &~ I~ ~""..J f:> (;J ,.,.f .:.ft:
/3
00 ' @
N C \-)irS
)\/1 red c. ~ (' pJ
L w"", te cl1 tfs i
ConS'lckr Qt'1 urn c.OYl-b:,f'\llI.5 N CVl'tf5> erf wf..rtfCt... M Qn 'fed o,c!.
QL:= N- M v (' wk,-k < SJ rr-er-e... ,
lNe v-cVl'-<l if'C- Yl c·l-1 i p.s \AI i.+A ovt Mlo cc mcV\+ fO Vl ~ N .
1) e +- 'I Jl e ()., (' (j til l4'\ V (;if' I C ~ ~
x I
~ ._"'~
/-
'# eF red <.,h 1 P>'f'" " _."
''vv~ 8~+
(~)( n~~) (¥) (~ )
iJ ! I ~) h1 Gl X l 0 JI'1- LI:s' k ~ ~ t';., r",.:> Hi)
\.> ' I'~
J~\S Yh eOjll.;S k == ko-th VI 0;.. d t-1
h?-oo+ 0+ ~+Or'(Y)v\\a... (¥). (S ,
Su PrOSe. We.. -fI~+ C-<lY1S,ekr- +k. sp.e CIC I CO$'e.. where.. o.ll ""H~ ch ipS
are ytd So
P(X=~),
Ihls ~15 -H-~ -SOr?'LCl. fYOh 1eM Ot-S
r fY'o I If h is~.~ C)~~ 01:': ~. ······,,~~~t~~J Q ". c.,QIf""""""
\Y\ by\ d ~~, red. chIp ~ 'vl~(n--t-\tvh1ft c~, ~ jIl..,.O/II "'-0 I'll/"+
bo we uSc. -#~ -pnl"'l cL1k of resfylc-ttJ ch 01((;.. 1M''';
PC X=H)~ (Y1)
(~)
B~t rx7 t~ h O~~1I' 1a he~ U k.. Lve. ho1.r~ ft> OJrSrJDr-.
~ CsK-. IN .).n..,-e ~ q rc
k <: n nc! r;/,qrJ . $'0 we...
hO'K ~ Ct-J:iO+r n-.k INn,k c\h 1J25 -, , - i7i7'-~--'''''''''''''' :'" .
- s,
5'<) c. ~ () ~ 7" ,~ IL j Gk "tJ
- ~. "•. lV~!j~.J ~ 1ar
e- Cc h S'vvh cJo l ~:C~Q.tL
n---k W'hvk C~t>J . ~: .. 'V""Ij:" , 1Y1-Ie ~.
So 4t (~lU~ J- ePvec4~
I:: 'f}J d .. t f.J /r' \ '''l ~ .V\ c~ '1~
. , (:·'· TI/·/·..... v~. _f .. ,c )ea~2J +h:~ avC- P
(~) tJ~~s I
n ChlfS ~,...... I
N c t-t tf-J ?O
. (:x) ~Il o~.
DIe- -F'nl~V\ If X 15 a dtJCyc:-k !ro~.,kW\
Val' ; C ~ I~ w;--li p~+ v4e-Fi~eJ.'v'
~ poZ)~ Il' +~ )( j.! SOld
~ ha \.rC.. h gu?er d € 0 we 1v-t~ J,:,-!vI ~ U--h-o '" L,..n* rell'c 1't-t +e......s n..) 1'1..JJ '
In +k --lex+- +-Ie pYhf IS de~
nrx3 n..) M) N) .'
, , . .' ... , ,,-" .. ' .".!.\;V'h t·, ab.. 0 U . I .ct, , + +.~"",e. cto .~,. d'i ,,,,;,/ oyJ~~~
. 1
I
'I
rn,~ (~ VI) (1)) . I J ,., I'max(Q;~-~ ~ k::=:
I \T~ '\ s ,c.~ I}j ~Lt?" S
\
(b.i)k::s.. hc~ n
(h-~) ~C)~ oCo-6. n-L :: k
SO-j.:s(~~ ? i t\Alt CC~+,··· C·'M~~S'e.k =5 n <.~
.
h't r..':l ~ +fa" Y') rt e:l c(y.rJ
hfCl1t>-.l'o. lA./t. ore t\,..Uj C ~ 0' ~ ''''j VI c.. "'" tfS /..... ~-te
<:::!-, ,~ b", ~ 9- ... $.. --H~ 6 r-e. 0""' lJ.J n rtel tIAIP·~ -C. V-J:)Q 5~ f~~
So -fte., above.... ,4P,¥C'c. '\ l'I, 11/ c I;+LcJ' f 9 qre. Ylec.C"Ssor;j_ ~+ -Flv:.s+'3lo",~
~~ It:)'\l k J'v +,fu. Ie.+ b-e e-4c..J'C 1+ k. .s c.+)~.f Ic ~ ~-II-e. c; ~ 0 v e.. -f-6l VG e.
" V' ~ v c Irfu ~ ~~ vi. c.. 0 "" Ct'¥-ttll""b ~ Cl
a Ii u do", d c: ~--f.) \l.(e.. ~ r-c r! c. L-... p" ' B-v..+ . w ~~+I. c ~ v I.A.+ --=±t-~ tv }.,d~ cjh Irs '\ W-e/. a ,V"'( 1"\ I+- ~ /'o-Q..
~ t-+.J ~ Q IJ' VII (l \Jt +'" e.- ~~ <::i ~~
n-k. k.Jl-tL-W /Ch..lp o ... J W-f~' (:) f'G. C> '" l'j L I l.vk! +r (' ""'}J C V 0. ! Ic ~~ {O tf 11-;" t::> L we 01}(' St.t M. k
I I J to.S-0 We i . y-y? '(, $, r l av"e
h- k :$!
L <;0.::;) Ie.? 11- L I i
Th"f..s: r.s~ -Ue.. St~ v-d I i-~i (,.. e Id'6
ot (b,..~). .JF ,-I- 'i..r Se+/S+tu!
we... CI2". ~ ... ~~.. 0 ked OJ;. d c.~-ol'l~ ~ h~ Ie ~"A~.-\':h (.Mr~ .Jt. -14 '''~ -- c il~' \'" (1,) 0'-e ~(,c('Jjollj o..JJuf'+I(I,.J.
t=1() po S ,-h-OY\ .. 2(}
S/,.t rr~ x has hjFtf~e<J~7v/C clt,s-h-- I ~ to -bYI iJ.J'-~ ri7 rc- ~ c4e-;.s
nJ n)N. ~
E( \/) ~ MV1(;1 A ... ' N~
ud V(X) = (N-h_) n .tJ. (I-~l N-I N tJJ
If <tJ<:,V fV+ I i , ~); .,
D'~ \t]' _--H-e- fYj~C~({l+.J c-f 5C'--Hu, I I N ()f red. oft ~ kOlA . "'l-. '..(1 f'-f d1f'04AI
l,,,,- a ~.f.) v'e ~ Ve. yYl e'J ,--t W (,-(;\ .-r t.
W rr- '" ~J c S '
r-C¥lfl'" JC~ ~ of~
~\'~11il ;Q I Jt rlrt bv-~4A.
~ ' \
;; 'I;
Th f'rre is Cf." o-Mr U OJ f-t,
dr:~iVe OK) ~ f~ VCj ve cb;//vrd
+I-t h ;*-0 r?' Jc: I dr s1YJ b,", -fc.::<>V( . ~1- i s _WO'~ hc;l"'~.
G-XCH")1E ~ T c Iu. n = 'L
p(x~ol;::: .~ L-J tV tV);
./""l~"':i) M' /tJ1!.~·!).""1':"
" . ' .. ' ;;; ",;ff ." ..,.~:,~ "" . '.'. .'. A" "'."" ;' / ~i.' ~~ ._... t
, ' - ~~.
~ f\J fV-I .'
. P( X'
P(x-- /) ::= p( R w) +P/WR)
:= M L +- ~M-iJ N ~I (J ;/:'1
::: ?!1 L tJ -
N-l
In :Jen ~r61J We-I clOt 1+1. +Pcoi- all I
+he tJJQr-ds w;~ k 1< ~o~J 11- h. kjj
hGlve.. -14.. So~ 'fJ'chc'tld-'j- InJuJ e a c h of --+1\ esc.. tVobc hr/,+u..J 0 ve .
{y(7 C~~J W l'.fA --f'J-e ...ro ~ J~)'IIf,~ •.:hr
tv(N- I) ,..Ii (IV - I )1'/
0 ... d -f-I,t t ~ h., tr··-e. -fI~ -S 0 "'" e -r; c ~Y'S 101 -Me n v IffIf b.rc -fu". S"VVa m 6(t. d. ~f
M 01-1) (I1-JJ-fJ) o~d. L (L-/) ---J (L-If-bf~ gv..t -fI~ c r:d?y aF -/I-e -Fe c10rs clo-er", 'f YJII e--f,ft.,. 5~ ~.
~..""",,\
P(X:::/c)=(;) P(R,,'R W'.;, t4)
:: (~) M(11-0 •.'- (f1-k-h2 L (L-I) ", ('=--)1-k+d Ie N{N- () , · at IV (-, n + I)
-WhJ,'s . ~7 ~he,o c/, -ft, +A~ ? ;2 3, (:~(\'1) (L r"-\~".
., , /::-. 11~{C) I
X) =
MfM--1 ., (f1-l:~l ) (L- I) .~. (L - III ~ t-tl )
--
:~.
e)( t-vc ,ie \.-1 ~e C ~-'~~ \
I \
(VI (~i) --' ( M- k I) L (L-I)- --(L"""l'fl-k~1 )1 _ Vl v
k---)' =
~ (t1~1& "~
-~ (AI-l~) < ~ ~ (~·N.-" +··t ) ~
\
(~) i
o Iov,-o'J~fJ~'-1h.. -(JrJ+- ;}4-wG'j c*') IS .(!e-Jier So If
~0\-( OYe ch fl"'-j a r't"el - W~V /J
PVbh It' Y1 (j" d !J '" IJ S%;.+ ,e+fr~
+hiJ'js ~f.tr:A" ~~k It/£e @K>C)
5 -fer 6c rk rf c; t3 l.(.C'f/.,)..j t' <!
CC!1 v\<; --/-k-FI rsf ~~ ~ d.
ilfshd. ~l)i t.v;I/~J ~
iYj ~co"J we-h~J. -Hrr:;+. I v I II +til 'j ~ ~ I) ¥"rht ) [(vf4y-,
FteClu.A~,\ (I IAJ~J tV~f'J b~t-e)
M~1;f of 'j 10"'- will fJ r~ -fI-< .si!<-o~ J .
C0~u~ ~t~J
,< •
GeJltcr-c!
sU j'? I~~ tJ ~(A",. d Va (,J .~ d'7 'f S
wi-M _ret 10 cr"",c",± fJl1d k+,X he... R h01""1 he.,- Df NJ c ;'drs
ij0'-t 3C.+' Whet+ dlsivlhv+c.u"
010 t s )( helle.. ?
/ h~'s €-)cr1oir/\S (0 /; f+Lt)
--I-k- fo~ J?'Vo /(;.f t:iYl Pa j e.. 02.}.
NolG --/i-oj- If N IS -far blj3v
~(lr f1 --fIerv J- TS c JJIf4~f l,to.. ti,v-'aw I~ 0/k-t r1 <:.{ w-c.t" +~ ~k urll ckts,.'1 ~-h ~ #,.(!f'J C'1t~ CI~(;fJ hevt, ~ ~~J hPC<llJ~ s:,.-~ ~~) !v,v-r.- ~ ~ rrJ ~
I.h -!J,IJ C6k- f
N- ~ ~ IV( (-;;) ..I _
N-I · .-.- .. ,--_.- ... - ~ W~ I f\/(1- 4 ) j) I
N- - I
( b~~.. tJ IS ),,4.,1J Q, ...L ex-...t '11 --
I
(jN N~
V(x7z n f~ (Je~ -fte,
}.u#".. 4-1- fj 2 I)