Last week I showed how to generate random points uniformly inside a 2-d circular region. That article showed that the distance of a point to the circle's center cannot be distributed uniformly. Instead, you should use the square root of a uniform variate to generate 2-D distances to the origin.
It is easy to generate random points that are uniformly distributed inside a rectangle. You simply generate independent random uniform values for each coordinate. However, nonrectangular regions are more complicated. An instructive example is to simulate points uniformly inside the ball with a given radius. The two-dimensional case is to
There are several ways to simulate multinomial data in SAS. In the SAS/IML matrix language, you can use the RANDMULTINOMIAL function to generate samples from the multinomial distribution. If you don't have a SAS/IML license, I have previously written about how to use the SAS DATA step or PROC SURVEYSELECT
