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.

- 2.1 Sample Spaces, Outcomes, and Events
- 2.2 Probability
- 2.3 Continuous Random Variables
- 2.4 Examples of Continuous pdf's