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2.3.2 Cumulative Distribution Function (cdf)

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).