Summary STAT 2000 Unit 2 Notes

probabilityproportionof
chapter 2 notes
timesthattheoutcomewouldoccurinaverylongseriesofrepetitionslongruncumulativeproportion
Lawoflargenumberstheaverageofasamplegetsclosertothepopulationaverageasthesamplesizeincreases
Trialoneiterationofarandomprocess samplespacesetofallpossibleoutcome in achanceprocess eventsubsetofsamplespace
Theprobabilityofanyeventis anumberbetweenoand inclusive Theprobabilitiesofallpossibleoutcomesmustsumto 1
probabilitymodeldescriptionofsomechanceprocessthat consistsoftwoparts asamplespaceanda probabilityfor eachoutcome
disjointmutuallyexilusive nooutcomesincommon venndiagramwithnooverlap independent outcomesdon'taffectotherscoin flip
validProbabilitymodelallprobabilitiesarenumbersbetweenoandi allprobabilitiessumto1 probabilitiesandoutcomesarepresent

keswords

pie niiioMiiaa
ititi
it
imieronability
complementrule Piota
GeneralAdditionRule manniiiiia i i
multiplication'uetorindependenteventstiti
likelihoodofanevent
p.it pp
happeninggiven
pirollinga2and tt p
conditionalprobability
another eventisalreadyknowntohavehappened
PlatBl 1199 PIBAl 19919

DependentEvents aneventthatoccurswhentheoutcomeofone PIAMBI PIA PIBA
eventintiveniestheoutcomeofanotherevent
aneventthatoccurswhentheoutcomeofone PLAIB
independentEvents
eventhasnoinfluenceontheotheroutcome
PIA orPIBIA PIB

measurementoftheoutcomeofachanceprocess comvousrandomvariablevalueinagivenrange height
randomvariablenumerical
values numberofheadsincointlips probabilityDistributionassignsaprobabilitytoeach
discreteRandomvariablefiniteordistinct value
expected valuemeanlongrunaverage EIXIEx.PH orvaluethatthevaviablecantakex probabilityofthat v ariable
NormalDistributiondistributionthatareapproximatelysymmetricandbellshaped EmpiricalRule681.111,95 12 99.71.13
standardNormalDistribution thenormaldistributionwithmeanoandstandarddeviation1 distributionofnormal2scores
savameternumericalsummaryofthepopulation statisticnumerical summaryofasampletakenfromthepopulation
samplingDistributiondistributionofvalues the
takenby statisticinall
p samplesofthesame
ossible sizefromthepopulation
stimulationusedtoestimatea samplingdistribution expertednumberofsuccesses np expectednumberoffailures ng




I
hm
É hÉon
phopty
f n p MYyYYjaimhetapshy9t
p
thismeanispwhenthedatacomesfroma randomsample
on
ape
center
thestandarddeviationofthedistribution ofPis l
thisiswhentheobservationsareindependent spread
testandseeitthesamplesizeislargeenough
101.7 isnotbigenough 103 isbigenough




thedistributionofx̅ isapproximatelynormalwhen
thepopulationisknowntobenormalor n 30 shape
thisisknownasthecentrallimittheorem
themeanofthedistributionof isM
hismeanismwhenthedatacomesfromarandomsample center
Misalsoknownasthepopulationmean
thestandarddeviationofthedistributionofx̅ is
thisiswhentheobservationareindependent
I spread


standarddeviation squarerootofthesamplesize