Rejection techniques: Basic rejection method Purpose Generate a sequence of random numbers which probability distribution function is f(x). f(x)is bound by c and defined on a finite interval [a, b f(x) Algorithm generate one uniform random number, sI, on(a, b)and one uniform random number, 52, on(0, c) 2) accept E1ifξ2f(ξ1)c; a 3)repeat the above process Geometric meaning SI and 5 are the coordinates of random points over the rectangle When we keep only 5i for the points below f(x), 5i has the probability distribution given by f(x)Rejection techniques: Basic rejection method: Purpose: Generate a sequence of random numbers which probability distribution function is f(x). f(x) is bound by c and defined on a finite interval [a,b]. Algorithm: 1) generate one uniform random number, 1 , on (a,b) and one uniform random number, 2 , on (0,c); 2) accept 1 if 2 f(1 )/c; 3) repeat the above process. Geometric meaning: 1 and 2 are the coordinates of random points over the rectangle. When we keep only 1 for the points below f(x), 1 has the probability distribution given by f(x). c a b f(x) x