3) Random variables with an arbitrary distribution function Let F(x)be the cumulative distribution function Remark F(x)is itself a random variable. Moreover, it can be shown that F(X) Is uniform random number on Algorithm 1) generate a uniform random number, 5I 2)22=F1(21) si is a random number with the cumulative distribution F(x) application This method is most useful when F-(x)can be obtained analytically3) Random variables with an arbitrary distribution function Let F(x) be the cumulative distribution function. Remark: F (x) is itself a random variable. Moreover, it can be shown that F(x) is uniform random number on (0,1). Algorithm: 1) generate a uniform random number, 1 ; 2) 2 = F-1 (1 ); 1 is a random number with the cumulative distribution F(x). Application: This method is most useful when F-1 (x) can be obtained analytically