A Simple Way to Generate Gamma Random Variates

For your assignment, you may need to generate random variates from a gamma(a,b) distribution, with density proportional to x^a-1exp(-bx). Here's one simple method, when a is an integer:

Generate a random variates uniformly distributed over [0,1). Call them u₁, u₂, ... u_a.
Compute L_i = -log(1-U_i) for i = 1 to a. Each of the L_i has the Exp(1) distribution.
Let S be the sum of all the L_i.
Return S/b as the gamma(a,b) random variate.

This isn't very efficient when a is large (there are better methods), but it's easy to implement.