all probabilities involving random variable can be computedin principlefrom its cumulative distribution function (cdf)defined by (xp[ ] cumulative distribution function for example [ bp[ bp[ af(bf(afigure shows generic cdf note that any cdf is right-continuousincreasingand lies between and figure cumulative distribution function (cdfa cdf fd is called discrete if there exist numbers and probabilities (xi summing up to such that for all (xi ( fd (xdiscrete cdf xi such cdf is piecewise constant and has jumps of sizes ( ) ( )at points respectively the function (xis called probability mass function or discrete probability density function (pdfit is often easier to use the pdf rather than the cdfsince probabilities can simply be calculated from it via summationx [ bf ( )xb as illustrated in figure figure discrete probability density function (pdfthe darker area corresponds to the probability [ bdiscrete pdf