A random variate is just a random number generated according to a specific probability distribution. It can also be referred to as a sample or observation. This chapter explains about engineering students generating random variates from probability distributions. Some specialized methods are also covered. The process of finding the Random Variate Generator (RVG) of a continuous random variable is systematic. A Bernoulli random variable is a discrete random variable that represents an experiment having two outcomes only. A geometric random variable is a discrete random variable that represents the number of Bernoulli trails needed before getting a success. A sample from a standard normal random variable with a mean of zero and variance of 1 can also be generated using the convolution method. Techniques for generating random variates from many important continuous and discrete probability distributions have been introduced and illustrated by examples.