Lecture 3 - Example 0+ tona;h-Oflfl| Pfflbu H...

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Unformatted text preview: Example 0+ tona;h-Oflfl| Pfflbu H pnpulu‘h‘on km N incl-‘Ju‘oluhls “(11‘ NF {'zmulm NS Smskna NFS female Smoktfs Take a. tangle.“ draw ) (ondi‘h‘onal on clawimj a SMokkr) fie Pmbhbi'fiy of ficfis‘ha 0k factual? {3 M P ( {’PMG‘? ‘ Snack”) —_- “:3 I. Dofmflfon of (ondih‘onat Pmbauhb 2 random G‘ffiw‘ Toss 0+ bind In}; 2. h‘mes. 04 "90‘ Head +wi¢e Irkdy m Tau ‘ ® (73 —9 Heal (ED ‘3 Tau't S = Samp'e Span—E— ’= 5"”17- 5P w. is. likely admin: H H m T "H H T 1/? '1 HH T H 2/9 '3 HT 3' 11' '/q 2 l H H 2.1 HH A: {11.5 23 H T 3’ PM): '/c-, 3| TH B; ' 32. TH , Gmn find “It?” {5 od' l9fi$+ J, B on? T, bu‘nd' i‘S Pmb.c{-A? 33 TT A B! L“. B; {Rf leaf-one 8’: {l3} 23) 3|) 3;) 33} -.-..-{HT, TH,T1~} Fr: {33} How +0 0S3§¢in prbb. in TM: mduwé sample {Puu {3 “f If 7‘? “‘"c'om drawn {5 Known +0 b? {mm B” we“ 9099‘ - ; It and . Ans_ ‘S Sufiufi’d by 232;; 0% d: euhmes is chumll.’ Pans) = PM) “5”” h 5" “‘8 “‘9 “'“W Hen“ ’ . ) _t_ 3. L“ 5 m 8 ‘1 + ‘1 + ‘i :: .L S In genera, 3.1m PMB) Ma P(s3)>o, define A I B) : I132} Remarks = - A (emolih‘unnl Prabalallfly (mncerns an MPeru'MPn/f' diH-ermt {Tim The 0r:5{nal tiph'fint’nf. A: Suck, {is [mpuhfldfl do” "‘1' from We Ought"; and Sit-mid be flfihfllec‘QS 0k dtfimzl‘fon. - Sim—k tmal.. prob. i5 jus‘l’ ordhmr, pmb. on a reduced Sample 59M). , all fie finnms about pmlzu'oilfl‘y remain UnICd (Md. “1- “Ac I 83 = I- PUHR] HAoBIc): PcmcHPmtc) _P(ABIC) P( ABlc) a \— [Pm‘m + P(8‘lc)J Examp‘e : _ Suppose playpr N In a [gr-{452 gene has akomd k={30{-H )K°{'D, find has many Hem-1's , 9-3. 6 . N is inhns‘leul Ca +3: anaLQlJ-iy find' 8 has ‘1‘ “Pour-+3. - Onfifind Sump/P 5pm.: : chose 1": ‘huu hcmds N '5 5) “Fr? are H: Oxd'anPS QGLL w. J'— N ) m a: { s Inns 4 hewfs } B: J‘ N. Kw. hand (#kands far 3 (\f‘h’r M has =. 62) /~ P( Pym-:Hve hound; mi. 1.1%”: 2 4-H'sfor5) = LlHZU/N my) P(AIB)= mam/pm) = L‘f 3: ( I3 - flannel Scxmp|e Spau : GNP“ N has hand In ’ 11:2 redneck Sample Spau km, .3) hauls for S. 32 05- 11959; has Q- ‘M’arh ; (DUMB) = QM?) L3"? 3.. use 0+ (malfhonal pate-LE}; h define fie Prob. of Oud‘tomt’s fin Gs tomP'FX QXP?V;MOf\t _ The mu\fip'ico€h‘on rule PMS) = Puma) Pm) [’(ABC) = PUHBC) (MRI) 2- P(B|BC) P(B|¢)P(C) —- If 0x (umPlex experflnl’nt (an be decomposPd hf‘b SQV'VN‘ 5+O~395 Sft. “it Pro]: I'n Oatk 51152 1': ans, +0 afiifin (unali'lfonul on ‘H’w Ou+tom95 of 11.9 Previous Star,“ 1 11m we use The mu|+iPl{tnflan rule in assiga Prob. 1‘!) He Ovd‘tomts OF 111? whs’f Qkpfi’rimrni‘. "" 11‘ “fr: [3 cum, GHQ! h5§;(’nml’f\,+ 1*“?- 35 {MSI‘StPfl/f fie“ (malfliunu bebnbflfl'u‘ls , it w“! be The Same as Hie one de‘l'vrmn‘avd by me mM'I-{phu‘h‘on rule Slump“ : Polya’s um model An urn {ooh-dun: b Hula 8: r rod balls A Ian“ I? drown ad- mndam , 3' fs replaced but in uddfl'ion , C brdls of- if: (0'0! (3 aJJE’J. SuPPose 0 draws were made , m‘nu‘l‘ {S The Fab. oi- o’efling n. Hack balls 7. ("d-n) (cn5249r an Outlome e = Lbbb-“b r-r-ur V'Y—fl “fir—fl n. (1,. L9. {333+ n1 (\re b‘fitk , +o“o'wod fit: n-fl. (0d . -— Q has .. .b. 5*" Inn—0c 1)‘, b?r+c b*r+Lnl-l)c r r+c . . __ r+fflr|2c bi-r-I- ma bra-(mun b+r+@-‘)c I _. cm? 0119; cud'tomP e 0031. fl. bluh balls has pmb- of Sam? form wffk “HM.- {nLTOJ'S in The numtfad'of in a Parmu‘lpd ordpr . _ mm. P( n. blank ban“: in n draws) = (1)130. D91 '- A Subuth 0+ Qat’n‘l‘s H.) Hz) ‘-- H” ;S & Eat‘l‘ih'an 0&- 1159 Sample Span {(3 Hwy are Mmfuully exclusiw .. N u) UH :8 km K If P(Hk) are known, Md {1‘ (mdfiid’nal on Gan-4x Hu’ He calmlu’rfcn of Pmbauu'h/ I'S €057; Then we can Me This Parfifion +5 Laden-lode H’u pmlo of ofipr Duon‘fs : For omy Qupnf A ’ Pm»: P(M§Hn)= NJAHK) N km N :1." Z P(AIHK) k3; TM: is («fled fie “ Law of To+al mama)" _. I ‘ trample ( Laflms rule of sutceSSmn ) Suppose Were are N+l urns umk has I: Mel and N'k NH}? be”: k: ‘13,!J - - - N (5005? am urn randomly , ‘Hien huh? Sutcessiue draws wfi'fi (Oplaumpwf' from If. Gwen find“ all {-am A draws are red, Wka‘l' f5. flw prob. fimd' Hw and draw will. aha be red 2 L9? A: 4 {fir-3+ A draws are (‘Qdk r3 = 01-1155- dvuw {‘3 Feel} PtBlA) = P(m3)/P(A) we now tu‘tulfid’? J P(Hl3) a. Pavhficflfl, —— Lei” HR = ‘{ um (‘3 ckose'n} “19% Ho H. --' HM fofn k pauh-fion ) J NM: -—'— N'f‘l P(AlH«)-: (-3)" HABIHk) : L) N ~ .5. NIJ‘C xk= N “Iva Xu=oi x,= JN') xa=fi ) X~=l 11- N is larse ) A: Kc," *X; =9; {5 small, N n l PM) = —” (z x ) ~j " u. - A _. x dx N-l-l Kao L ) o n+l swim, 9mg) 5:. 3'3 P(Blfi)g "1“ IT- Nl‘s far,9. ...
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This note was uploaded on 01/13/2010 for the course STATS 116 taught by Professor Staff during the Spring '07 term at Stanford.

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Lecture 3 - Example 0+ tona;h-Oflfl| Pfflbu H...

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