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2 An Introduction to Probability and Statistics

An essential component of a Monte Carlo simulation is the modeling of the physical process by one or more probability density functions (pdf's). By describing the process as a pdf, which may have its origins in experimental data or in a theoretical model describing the physics of the process, one can sample an ``outcome'' from the pdf, thus simulating the actual physical process. For example, the simulation of the transport of 2 MeV neutrons in a tank of water will necessitate sampling from a pdf that will yield the distance the neutron travels in the water before suffering a collision with a water molecule. This pdf is the well-known exponential distribution and is an example of a continuous pdf because the outcomes (distances to collision) are described by real numbers. The exponential distribution will be described in more detail later in this chapter. On the other hand, the simulation of roulette will require sampling from a discrete pdf that describes the probability of obtaining one of the 37 (36 outside the U.S.) numbers on a roulette wheel.