m16813 Continuous Random Variables: Summary of The Uniform and Exponential Probability Distributions 1.10 2008/06/06 12:51:29 GMT-5 2009/02/20 10:17:38.120 US/Central Susan Dean Susan Dean deansusan@deanza.edu Barbara Illowsky Barbara Illowsky, Ph.D. illowskybarbara@deanza.edu Susan Dean Susan Dean deansusan@deanza.edu Barbara Illowsky Barbara Illowsky, Ph.D. illowskybarbara@deanza.edu Connexions Connexions cnx@cnx.org Maxfield Foundation Maxfield Foundation cnx@cnx.org continuous distribution elementary exponential formula probability random statistics summary uniform variable Mathematics and Statistics This module provides a summary of formulas and definitions related to Continuous Random Variables. en Formula X = a real number between a and b (in some instances, X can take on the values a and b). a = smallest X ; b = largest X X ~ U(a, b)The mean is μ a+b 2 The standard deviation is σ (b-a)2 12 Probability density function: fX = 1b-a for a X bArea to the Left of x: P(X x) (base)(height) Area to the Right of x: P(X x) (base)(height) Area Between c and d: P(c X d) (base)(height) (d-c)(height) . Formula X ~ 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, X 0 Area to the Left of x: P(X x) 1- e-m⋅x Area to the Right of x: P(X x) e-m⋅x Area Between c and d: P ( c X d ) = P ( X d ) - P ( X c ) = ( 1 - e − m⋅d ) - ( 1 - e − m⋅c ) = e − m⋅c - e − m⋅d Percentile, k: k = LN(1-AreaToTheLeft) -m