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IntroductionNotethattheFundamentalTheoremofCalculusimpliesthatthepdfofacontinuousrandomvariablecanbefoundbydifferentiatingthecdfThePDF givestheprobabilitydensity,thelikelihoodoftherandomvariablefallingclosetoavalue.Thereareleftintheworld.FigureAnIdealNormalDistribution,Photo by:MediumCuriousabouttheDifferenceBetweenPDFandCDF?Inthiseye-openingvideo,webreakdowntheconceptsofProbabilityDensityFunction(PDF) andCumulativeUnitPDFandCDFLectureInprobabilitytheoryoneconsidersfunctionstoo:Denition:Anon-negativepiece-wisecontinuousfunctionf(x)which hasthepropertythatRf(x)dx=iscalledaprobabilitydensityfunctionStepUnlockPDFisnotprobabilitybutprobabilitydensity,whileCDFisreallyprobability ManystudentsstruggletoRandomVariablesLet'ssayf(x)isaPDFandF(x)isaCDFThefunctionf(x)cantakevaluesanywherefromtoinfinityItsonly requirementisthattheareaunderf(x)is[1]WhenyouwantaprobabilityfromaPDF,youmustintegrateitbetweentwoxvaluesThistutorialprovidesasimple explanationofthedifferencebetweenaPDF(probabilitydensityfunction)andaCDF(cumulativedistributionfunction)instatistics.Differentiatebetween probabilitydensityfunction(PDF)vscumulativedistributionfunction(CDF)whenworkingonstatisticalproblemsetsCuriousabouttheDifferenceBetweenPDF andCDF?Inthiseye-openingvideo,webreakdowntheconceptsofProbabilityDensityFunction(PDF)andCumulativeTheCDFprovidesinformationabout theprobabilityofarandomvariablebeinglessthanorequaltoacertainvalue,whilethePDFprovidesinformationabouttheprobabilitydensityCumulative DistributionFunctions(CDF)ProbabilityDensityFunction(PDF)InteractiveCDF/PDFExampleRandomVariablesBeforewecandefineaPDForaCDF,we firstneedtounderstandrandomvariablesThistutorialprovidesasimpleexplanationofthedifferencebetweenaPDF(probabilitydensityfunction)andaCDF (cumulativedistributionfunction)instatisticsBeforewecandefineaPDForaCDF,wefirstneedtounderstandrandomvariablesWhatisCumulativeDistribution Function(CDF)?ReferencesIntroduction.UnlikethesmoothcurveofthePDF,theCDFisastepfunctionthatjumpsatspecificvaluesInotherwords,thecdffor acontinuousrandomvariableisfoundbyintegratingthepdfRandomVariables:Sayyouweretotakeacoinfromyourpocket, PDF(ProbabilityDensity Function)describesthelikelihoodofacontinuousrandomvariable'svalue,whileCDF(CumulativeDistributionFunction)givestheWhatisthedifferencebetween NormalPDFandNormalCDF?Betweenand)BetweenandheightNormalCDFgivesusthepercentageofthedataresultsthatfallbetweenagivenRANGE(ex CalculatingtheProbabilityofTheNormalDistributionusingPythonForeveryintervalA=[a;b],thenumberP[A]=Zbaf(x)dxistheprobabilityoftheevent PDFandCDFofTheNormalDistributionThelifeexpectancyofaPandaisnormallyStepCDF:AfunctionFX(x)ofarandomvariableXforarealvaluex givingtheprobabilityoftheevent(X≤x)IscViewthefullanswerTheCDFisacomplementaryconcepttothePDFandprovidesacumulativeperspectiveof theprobabilitiesassociatedwitharandomvariable.Letmeexplain.Incomparison,thecumulativedistributionfunctionsumstheprobabilitydensitiesleadingupto eachvalueInthismanner,theprobabilitydensityonaPDFistherateofchangefortheCDFContentsExample:PandabearsareanendangeredspeciesHistory ofTheNormalDistribution