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f(x)={ba,0,fora≤x≤botherwiselookslikethis:f(x)b-aXabDefinitionArandomvariableXhasauniformdistributiononinterval[a,b],writeX uniform[a,b],ifithaspdfgivenby.Theuniformdistribution(alsocalledtherectangulardistribution)isatwo-parameterfamilyofcurvesthatisnotablebecauseit hasaconstantprobabilityInprobabilitytheoryandstatistics,thecontinuousuniformdistributionsorrectangulardistributionsareafamilyofsymmetricprobability distributionsTheuniformdistributionisalsosometimesreferredtoastheboxdistribution,sincethegraphofitspdflookslikeaboxSeeFigurebelowContinuous uniformdistributionAllvaluesinthedistributionhaveaconstantMissing:pdfMatlabtemplate:UniformPDF•Stats=????;•r2=???+???*rand(Stats,1); •disp(mean(r2));•disp(var(r2));•disp(std(r2));•step=;•[a,b]=hist(r2,0:step:8);•pdfe=a/sum(a)???Acontinuousuniformdistributionisatypeofsymmetric probabilitydistributionthatdescribesanexperimentinwhichtheoutcomesoftherandomvariablehaveequallylikelyprobabilitiesofoccurringwithinaninterval[a, b].UniformDistribution.Theprobabilitydensityfunction(pdf)ofacontinuousuniformdistributionisTheuniformdistributionisacontinuousprobabilitydistribution andisconcernedwitheventsthatareequallylikelytooccur.TheUniformorRectangulardistributionhasrandomvariableXrestrictedtoafiniteinterval[a,b]and hasf(x)hasconstantdensityovertheintervalItistheuniformdistributionon[0;1]AcontinuousrandomvariableXhasauniformdistribution,denotedU(a,b),if itsprobabilitydensityfunctionis:f(x)=b aAcontinuousrandomvariableXhasauniformdistribution,denotedU(a,b),ifitsprobabilitydensityfunctionis:f(x) TheuniformdistributionisacontinuousprobabilitydistributionandisconcernedwitheventsthatareequallylikelytooccurRandomnumbergeneratorsin computersrstofallgeneraterandomnumberswiththatdistribution[1]UniformDistributionsWhenworkingoutproblemsthathaveauniformdistribution,be carefultonoteifthedataisinclusiveorexclusiveofendpointsAuniformdistributionisacontinuousrandomvariableinwhichallvaluesbetweenaminimumvalue andamaximumvaluehavethesameprobability.ThetwoparametersthatdefinetheUniformDistributionare:aa=minimumbb=maximumTheuniform distributionon\([a,b]\)isdenoted\(\mathcal{U}[a,b]\),andhasPDF\[p(x)=\left\{\begin{array}{lr}1/(b-a)&:x\in[a,b]\\&:xotin[a,b]\end{array} \right\]TheuniformdistributionisasymmetricprobabilitydistributionwherealloutcomeshaveanequallikelihoodofoccurringUniformDistributionUniform DistributionsWhenworkingoutproblemsthathaveauniformTheuniformdistributionisasymmetricprobabilitydistributionwherealloutcomeshaveanequal likelihoodofoccurringInMathematica,yougetsuchDenitionUniformDistributionAcontinuousrandomariablevV)(Rthathasequallylikelyoutcomesoverthe domain,adistributionOverview(*TheUniformDistributionSuchadistributiondescribesanexperimentwherethereisanarbitraryoutcomethatliesbetween certainboundsAllvaluesinthedistributionhaveaconstantprobability,makingthemuniformlydistributedfortwoconstantsaandb,suchthatapdf