12. Suppose it is easy to generate random variable from any of the distribution F, , i = I, . . . , n. How, can we generate from the following distributions? F(x)=IT, F,(x) (b) (a) F(x) = 1-IT-i [1-F,(x)] l Hint: If Xi, i = I, . . . , n, are independent random variables, with Xi having distribution Fi, what random variable has distribution function F?] 13. Using the rejection method and the results of Exercise 12, give two other methods, aside from the inverse transform method, that can be used to generate a random variable having distribution function Discuss the efficiency of the three approaches to generating from F. 12. Suppose it is easy to generate random variable from any of the distribution F, , i = I, . . . , n. How, can we generate from the following distributions? F(x)=IT, F,(x) (b) (a) F(x) = 1-IT-i [1-F,(x)] l Hint: If Xi, i = I, . . . , n, are independent random variables, with Xi having distribution Fi, what random variable has distribution function F?] 13. Using the rejection method and the results of Exercise 12, give two other methods, aside from the inverse transform method, that can be used to generate a random variable having distribution function Discuss the efficiency of the three approaches to generating from F