OPRE 3360_Ch5.pdf - OPRE 3360 Managerial Methods in...

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OPRE 3360 : Managerial Methods in Decision Making Under Uncertainty OPRE3360‐ ©Naseri 1
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Chapter5:DiscreteProbabilityDistribution InthisChapterwewillcombinetheprinciplesofdescriptivestatistics (Chapter2and3)andtheprinciplesofprobability(Chapter4). Wewilldetermineprobabilitydistributionswhichwilldescribe what willprobablyhappen instead of  whatactuallydidhappen . Thecoreof inferentialstatistics isbasedonknowledgeof probabilitydistributions 2 OPRE3360‐ ©Naseri
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RandomVariables RandomVariable Avariable(typicallyrepresentedby ݔ )thathasasinglenumericalvalue, determinedbychance ,foreachoutcomeofanexperiment DiscreteRandomVariable Arandomvariablewhichcanonlytake acountablenumber ofvalues. ContinuousRandomVariable Arandomvariablewhich cantakeinfinitelymanyvalues .Itisassociatedwitha continuousscale. 3 OPRE3360‐ ©Naseri
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Example: DiscreteRandomVariablewithaFiniteNumberofValues Let =numberofTVssoldatthestoreinoneday, where ݔ cantakeon 5 values ሺ0, 1, 2, 3, 4ሻ 4 WecancounttheTVssold,andthereisafiniteupperlimiton the numberthatmightbesold(whichisthenumberofTVsinstock). OPRE3360‐ ©Naseri
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Let =numberofcustomersarrivinginoneday, where ݔ cantakeonthevalues 0, 1, 2, … 5 Wecancountthecustomersarriving,butthereisnofiniteupper limitonthenumberthatmightarrive. OPRE3360‐ ©Naseri Example: DiscreteRandomVariablewithanInfiniteNumberofValues
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Exercise:RandomVariables 6 Question Random Variable x Type Family Size x = Number of dependents reported on tax return Distance from home to store x = Distance in miles from home to the store site Own dog or cat x = 1 if own no pet; = 2 if own dog(s) only; = 3 if own cat(s) only; = 4 if own dog(s) and cat(s) OPRE3360‐ ©Naseri
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DiscreteProbabilityDistributions ProbabilityDistribution Theprobabilitydistributionforarandomvariableisdefined byaprobabilityfunction,denotedby ( ),whichprovides theprobabilityforeachvalueoftherandomvariableand describeshowprobabilitiesaredistributed overthevalues oftherandomvariable. 7 OPRE3360‐ ©Naseri
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