Transcription of Session 2: Probability distributions and density …
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Session 2: Probability distributions and density …
Session2: p. :Probabilitydistributionsanddensityfunct ions p. :Probabilitydistributionsanddensityfunct ions p. 3 RandomvariablesSession2:Probabilitydistr ibutionsanddensityfunctions p. 4 RandomVariablesA randomvariableis ,thevalueofthefirstrollofa ,thesumofa rolloftwo ,therollofa dice,ortheoutcomeofahorserace, ,thenumberofwhitehaironmyhead,orhow muchdividendINFOSYSTCH willannouncenextyear, :ContinuousRVscanhave a fixedminimumormaximum,however, :Probabilitydistributionsanddensityfunct ions p. 5 ProbabilitydistributionsSession2:Probabi litydistributionsanddensityfunctions p. 6 Whatis a probabilitydistribution?Fora discreteRV, theprobabilitydistribution(PD)isa ,intherollofa die:ValueProbabilityValueProbability11/6 41/621/651/631/661/6A probabilitydistributionwillcontainallthe outcomesandtheirrelatedprobabilities, :Probabilitydistributionsanddensityfunct ions p. 7 Howtoreada probabilitydistribu-tionFromthedistribut ion,wecanfind:X = 3Pr(X= 3) = 1=6X = evennumberPr(X= 2orX= 4orX= 6) = 3=6 = 1=2 Moreinteresting,wecanalsofind:Pr(X >3) = 3=6 = 1=2 Thisis calledacumulative :Probabilitydistributionsanddensityfunct ions p.
What is a probability density func-tion? The probability density function (PDF) is the PD of a continuous random variable. Since continuous random variables are uncountable,
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