Distributions July 27g 2020 Distribution Geometric 1 The Copoun Collector's problem Application Poisson Distribution 2 Question number of times is the expected we have what 6 sided die until we roll a fair roll to a 63 55 prew 65 bhim F 7 o Li
1 Geometric Distribution with Pr HJsP until we get H Flip coin a Is X until the number of F r flips the first t Heads appears pr 9 P Pr for instance was H WITH u p p k t I U PYP T TH Xvi I wz i i Pr I Then X A random variable for which Definition Pr Asif Ci pyo p the geometric distribution with said Is to have parameter P Geometric LP X Eod Fa Pr xsz T.si Sanity check 10 IE Chigi P PEELE u Ps Px p p prqtyyz.jp Pxp I
X If P Geometric E Me Varix a PrExsa iprcxsigs.fi gPf Ect For An Geometric Theorem i y P tu Pisa.p i ECD II PREM D g g N p Ei Phx i prcxz.iq PREF E I E j I me jst E zprcxzi3 SE EiprEx3ieDsE9iPrcxs.i3 E7ci DPrExs.i EI prcxzizli IED zfprcx.si I I E l P Alternatively p 3pct PP 4pct Ppe E EX Pe 2Pa P z 2pct Pfe 3pct PP C P ECX3 P Pu O Pll Ps3 Pu Pfe P pet P PEED Ice pg 5 PEExJ l P EEx3
Remember EEXJsaq.ua Pr EXIST for V.V X Then Y LOTUS Define V.v Y Guy a agca PrCX a3 E gcxD EEY3 function 2 ECM Vara EEx 7 i2prcx i3 Efi ki p p EEE 1611 PPPs P e I U P P 9 et PTP EEE l PPP e l PIP a P EEN l P P 9 4 o x v tr g l PFP l PPPs PE EXT P 3G Pj Pe 5 7 w w l p I l2i 1 p z 2 AE ics pyMp zf u pJi p I EEK 2 I PEER ECXT z f tofpgsovarlN i eepg.EE epa Ip tpz pz pt f
collectors Problem The coupon in different types of baseball cards There are the cards by buying boxes of cereal we get contains exactly one eard Each bon is equally likely to be any card This n cards of the Sh we need to buy in The number of boxes collect all n cards order to What Eton is of cards Define Xis we buy before WE get the ith new card Then Xn X Sn Xz EE.EE tiJsE.ECXiI E Csn so the distribution for what Xi is
Xi lxPr AED a I D E XD Prc x Xz Pr old 3 Xz pre new Eid Ten nz Geometric C EXT I l h X 38 old card 2h pr Geomteric frenzy 3 Proven card nz I E EX 37 Z n i Xi 8 old card Pr Pre new card I fxinGeometrianizing th EExi n d D h E'T En Ect i3 EI E Csis i 9 a exercise
2 Poisson Distribution The average number of passing cars Assume a tunnel per aint time is X Passing through X The number of Define cars Passing per unit time probability distribution of X what is the Question Poisson distribution A random variable Definition for which Iso prEx e on is said Poisson distribution to have An Poisson X SPREED L check Sanity is 0 Eyre xsis.ES xeI E.E I Exe U w I e
is what S EEN the average t e i.E.EI eext.EE e ie EiI.a Is e Ei de txe d Var What X about 2 C Ex EEN var X EE iI e em Efi Ei uzEn e t.Eii i e es EI e iEEn.te iE e in.E i.e i.ie e it.EE I e taE i e e
Ethel 14h EEx9 He e E Existed 432 1 Varcx EEP varcxj.FI Poisoned and Yu Poisson X Theorem Let Poisson random variables be independent Tay Then Poisson hey Z Hey e Her K PIE Proof Pr Zsk Pr Ysk total Probabeity x n E Pr f I t K I Iso Jindefenden Eko PVEX izxprcys.LI iExI n E e K i i K disk e UN 1 z i CK D Iso I
der Iii k e Cher i K air E e GK e Her of Binomial a Limit Poisson as Xu Binomial Ln In Theorem where Let a fixed constant Then A is h Paris E n a proof of f pi Ci Psi Pr if Pstn a testing do idea that The is we on and A success we get many sample Points n for the events the of occurrence n is defined X so sample points nRss rateT we can get where don't but p know we it by testing many Crusoe estimate of an
and the successful event Points counting as A Xu Binomial hi so Pstn of now limit take the we vi oo premise 7 LET u 5 i u Inna Es h ni o in a n hm n n Ct ET Et bi Ct d Isi Ct ET prcxsidsk.at xe dxi prcxsiss.IE
Recommend
More recommend
