Programming Simulation
Summary
EG 381: Probability Team Projects
Simulation and modeling are very important tools for engineers and scientists. One such technique is called "Monte Carlo" simulation. This is a class of algorithms which obtain numerical results (simulations) by repeated random sampling. This random sampling is done with a random number generator (RNG) (or pseudo-random number since it is not truly random if it is generated by a deterministic process, the generator algorithm). For example repeated calling a (uniform) random number on the interval [0,1] from the RNG and assigning it a value of H for heads if the number is less than or equal to 0.5 or T for tails if it is greater than 0.5 is a Monte Carlo simulation. What this does is divide the interval between [0,1] inclusive into two equal parts and thereby giving us an effective probability of p(H) = 0.5 and p(T) = 0.5. One of the earliest uses of this technique was in simulating the probabilistic chain reaction cascade of the fission of heavy isotopes in the atomic bomb.
Simulation and modeling are very important tools for engineers and scientists. One such technique is called "Monte Carlo" simulation. This is a class of algorithms which obtain numerical results (simulations) by repeated random sampling. This random sampling is done with a random number generator (RNG) (or pseudo-random number since it is not truly random if it is generated by a deterministic process, the generator algorithm). For example repeated calling a (uniform) random number on the interval [0,1] from the RNG and assigning it a value of H for heads if the number is less than or equal to 0.5 or T for tails if it is greater than 0.5 is a Monte Carlo simulation. What this does is divide the interval between [0,1] inclusive into two equal parts and thereby giving us an effective probability of p(H) = 0.5 and p(T) = 0.5. One of the earliest uses of this technique was in simulating the probabilistic chain reaction cascade of the fission of heavy isotopes in the atomic bomb.
CollapseLearning Goals
The main learning are the ways in which simulation can complement theory and can provide more intuitive insight and visualization into a problem.
Context for Use
I use this project in a junior probability and statistics course for engineering majors. The students should have had a semester's exposure to MATLAB and/or programming generally.