Generating Binomial Random Variates
Methods for random number generation where the marginal distribution is a binomial distribution are well-established.
One way to generate random samples from a binomial distribution is to use an inversion algorithm. To do so, one must calculate the probability that P(x=k) for all values n through k. These probabilities should sum to a value close to one, in order to encompass the entire sample space. Then by using a Linear Congruential Generator to generate samples uniform between 0 and 1, one can transform the calculated samples U into discrete numbers by using the probabilities calculated in step one.
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