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3 Sampling from Probability Distribution Functions

As described earlier, a Monte Carlo simulation consists of some physical or mathematical system that can be described in terms of probability distribution functions, or pdf's. These pdf's, supplemented perhaps by additional computations, describe the evolution of the overall system, whether in space, or energy, or time, or even some higher dimensional phase space. The goal of the Monte Carlo method is to simulate the physical system by random sampling from these pdf's and by performing the necessary supplementary computations needed to describe the system evolution. In essence, the physics and mathematics are replaced by random sampling of possible states from pdf's that describe the system. We now turn our attention to how one actually obtains random samples from arbitrary pdf's.

This chapter will consider sampling from both continuous and discrete pdf's. Table 1 summarizes the important properties of both types of pdf's.

Table 1: View.

We will now discuss how to obtain a random sample x from either a continuous pdf or a discrete pdf .