The cumulative distribution function gives the probability that the r.v. is less than or equal to x:
Note that since , and the integral of is normalized to unity, obeys the following conditions:
Figure 5 illustrates a representative cdf. Note the dependence of as . Since is the indefinite integral of , . The cdf can also be defined for a discrete pdf; however, this will be deferred until we discuss the subject of sampling from a discrete distribution.
Figure 5: Representative Cumulative Distribution Function (cdf).