continuous cdf cdf fc is called continuous if there exists positive function such that for all fc (xf (udu ( pdf note that such an fc is differentiable (and hence continuouswith derivative the function is called the probability density function (continuous pdfby the fundamental theorem of integrationwe have [ bf(bf(af (xdx thuscalculating probabilities reduces to integrationas illustrated in figure figure continuous probability density function (pdfthe shaded area corresponds to the probability [ ]with being here the interval (abremark (probability density and probability massit is important to note that we deliberately use the same name"pdf"and symbolf in both the discrete and the continuous caserather than distinguish between probability mass function (pmfand probability density function (pdffrom theoretical point of view the pdf plays exactly the same role in the discrete and continuous cases we use the notation distx and to indicate that has distribution distpdf and cdf tables and list number of important continuous and discrete distributions note that in table is the gamma functiong( - xa- dxa in advanced probabilitywe would say "absolutely continuous with respect to the lebesgue measure