Continuous Random Variables: Summary of The Uniform and Exponential Probability Distributionsm16813Continuous Random Variables: Summary of The Uniform and Exponential Probability Distributions1.102008/06/06 12:51:29 GMT-52009/02/20 10:17:38.120 US/CentralSusanDeanSusan Deandeansusan@deanza.eduBarbaraIllowskyBarbara Illowsky, Ph.D.illowskybarbara@deanza.eduSusanDeanSusan Deandeansusan@deanza.eduBarbaraIllowskyBarbara Illowsky, Ph.D.illowskybarbara@deanza.eduConnexionsConnexionscnx@cnx.orgMaxfield FoundationMaxfield Foundationcnx@cnx.orgcontinuousdistributionelementaryexponentialformulaprobabilityrandomstatisticssummaryuniformvariableMathematics and StatisticsThis module provides a summary of formulas and definitions related to Continuous Random Variables.enUniformX = a real number between a and b
(in some instances, X can take on the
values a and b).
a = smallest X ; b = largest XX ~ U(a,b)The mean is
μa+b2The standard deviation is
σ(b-a)212Probability density function:fX=1b-a
for
aXbArea to the Left of x:P(Xx)(base)(height)Area to the Right of x:P(Xx)(base)(height)Area Between c and d:P(cXd)(base)(height)(d-c)(height). ExponentialX ~ Exp(m)X = a real number, 0 or larger.
m = the parameter that controls
the rate of decay or decline
The mean and standard deviation are the same.μ=σ=1m
and
m=1μ=1σThe probability
density function:f(X)=m⋅e-m⋅X,
X0Area to the Left of x:P(Xx)1-e-m⋅xArea to the Right of x:P(Xx)e-m⋅xArea Between c and d:P(cXd)=P(Xd)-P(Xc)=(1-e− m⋅d)-(1-e− m⋅c)=e− m⋅c-e− m⋅dPercentile, k:k=LN(1-AreaToTheLeft)-m