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# Midterm #1 Study Guide - Probability Theory and Statistics 3341

UTD

GPA 3.3

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## About this Document

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This 7 page Study Guide was uploaded by Michelle Schmutz on Sunday January 31, 2016. The Study Guide belongs to 3341 at University of Texas at Dallas taught by Dr. Mohammed Saquib in Winter 2016. Since its upload, it has received 101 views. For similar materials see Probability Theory and Statistics in General Engineering at University of Texas at Dallas.

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Date Created: 01/31/16

Midterm #D StudyGuide Definitions - a groupfthings c- swung in into Ⱦ U ,"or" XEAVBiff*andXEB Somethingwithtwo restrictions itmust satisfyt leastone " n ," and, C XE AAB iffXE A and XEB Somethingthat'salways partof anotherthingthat it cannot exist withou. Ⱦ X E A ' if× A Monieal oppositesndwhait'no. TU set ¥ H - n Ain -01it € Aj thetj Can neverbe together or happen same time Ⱦ AsUAZU An 㱺 ..V The parts the whole ofn't overlap,but all the pieces add up to a picture ,oorthe set. of Ai,..,An Theparts make a whole (collectivelyaustive, but don't overlap atall (mutuallytexclusive) Universals Allofthepossibilitiesanbe consideria situation Element aset Fsingubr partof : observation Outcome Any possible of an experiment . : a set an Event of outcomes of experiment the - mutuallyexclusivecollectivelyaustive &SampleSpa= setineall grain outcomes , of possible *Dependent :theproperty one eventchangingthe Occurrenceoanotherevent PCAH P(t B) & IndependentOccurrence one eventdoesn'tchange/influence the likelihood another eve.Thislsomeatheymusinters.ct PCA)=P (AIB oȾ Pfaff㱺 PLB) =PLAMB) Rules , Laws & Axioms , De 's law Setandprobabilitykeot -4 Morga- element outcome CAUBJEACABC universaset || Set fugitpace ~ 1Let XECAUBT W 㱺 , general in an experiment 㱺 XEAUB ×€AdX#B ' 㱺 xEA4×eB §÷e÷¥¥I£I¥i㱺 Bayes Rule manta .ee#* PCS A,iomsA) 20 - Nowbltd how smalleverythingthinhesample has achance Ⱦ P(0)=O , space ofoccurring 2 - )=1 Alloutcomesoccurithinhe Sample space Ⱦ a Ac =P(D=1=P( AUAD =PCA )+p(A= ftp.zpat 3 Ⱦ - AiAj=0 ; i=j sum ofthe propertiesPTAUAZU.)=PtAD+MA..Path Ⱦ PCAU B) A B ABK - BAL ! B A=AB' UAB p*±RaHtrAA PCAUBH .tt#tbBUABpatI}kBoft2B=BA' I I µ PBHEPCBAIHCAB) ) + PCHCA + PCABHKAD B) -PCAB =PCH+P( ) * reopens • ( A 2) P ( Ai U Az ) =p A i)+ p ( The to Union Ai and Az is equal the addition of A i and Azof, both which the universal set. of equal • If A = A U Az U .. .U Am and Ain ¥0 for then Aj itj , Ptt ) =§s PGD If the sets are collectively exhaustive and exclusive then the mutually , probability set A is to the summation all the of equal 1 and at of of parts of A , starting at ending M . : • P E ] ( probability measure ) Satisfies - P[0 ] = 0 There are 0 elements within an empty Sample -P A'] = - P [ A] space [ Setnd its the entire complement makeup sample space , whether there are other sets or not . If Something takes the up entire sample space , it isequal to 1 , since we are about a whole . talking parts of - For A and B P [A UB ] =P [A ]tP[B ] - P [ A AB ] ( doesn't have to be mutually any , When the a union to exclusive ) finding probability of , avoid counting what overlaps twice , subtract the intersection - If A C B ,then P (A) EP (B) * A is If within B , then the property of A B MBHKAUBAC ) is less than or to the A = PCAHPCBA 9>-0 equal property of B . ' NBA) =P (B) • The an event B = { si sz .. . Sm } is the sum the probability of , , , of the outcomes contained in the event . probabilities of P (B) =¥sP[{ si }] an event is the sum its outcomes . of • For an with = { 5 ... Sn } where outcome si experiment sample spaces , , , each , is lively. unless restrictions are stated all the outcomes have equally , si ) = 1£ i En . an efud chance . P ( £, of occurring • Fara partition B= (Bi ,Bz,,..) and events in the sample ,ktCs=AnB .For itjitheevents saree anyexclusive and A=GUCzU ... Ciandcj mutually PCAKPCGU ...Ucn ) *PCAB)=pCB)PCAfB ) = PCC ,)t.. .tPKn) =p(tABn,)t..tPCABnw)T otdPnbabili BDPCAAB =*P( • For any eventA , and partition( Bi,Bz ,..,Bm ), MHFE ,.PtAnBD • Ahexperimentconsistsytwosub experiments. Ifonesub experiment has K outcomes andtheothersubexperimehthasn outcomes, then theexperiment hasNK outcomes. • Themembesqk . permutations distinguishable objectsis qn (N Nt N -4 .CN -KH )=NL N=# of distinguishableobject )k=N( )( . ! K=#q objects weare E, - N (Nt 's interestedn. (N )K=# ⾨Ez - Ny (N )v=# ofwayswecangetk object \ 㱺 ofwayswecangetnobjectoutytl Ek - (N-k+D reorderingNamongstitself ( Nhingnftgyxnjfjnfnkslxwhk .. .×1=wN÷hy .on That when ordermaters • distinguishablejectsis Themumberqwaystochooxkobjedsoutqn Kfwn¥r¥w# .Y Earmuff widow T T doesn'tmates "Nchoosek" objective Generalizatioof #dovitoreatow successesandfailures torn tests Baye 's-Theorem ooa PCBAAHPCBPCAABT The conditionalprobability PCA) Occuranuqtheeventb . ) *Poftheeveuttgiventhe )=P( I *P(AtB=pCBPL 㱺 # IAPB )=PBB( PAA)P( ) a PTD PCBA conditionprobability

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