![]() Monte Carlo simulation is a versatile and valuable tool in the business world. You draw n random sample ( x, y) within ( 1, 1) and you count the number of x 2 + y 2 < 1. Sears uses this method to determine inventory needs, while financial planners use it to optimize investment strategies for their clients’ retirement. Suppose we are using Monte Carlo simulation to estimate the pi. The activity that follows was inspired by those simulations and was used by my AP Physics class last year with very good results. GM uses Monte Carlo simulations to forecast net income, predict costs, and manage risk. 3 It is my belief that this method may be easily related to the students by performing the simple activity of sprinkling rice on an arc drawn in a square. It has been calculated in hundreds of different ways over the years. \(\pi\) is the mathematical constant, which is equal to 3.14159265, defined as the ratio of a circle’s circumference to its diameter. Other examples where this method was applied were typically done with computer simulations 2 or purely mathematical. In order to estimate the value of Pi using Monte Carlo simulation it is necessary to determine the region whose area is to. To better understand how Monte Carlo simulation works we will develop a classic experiment: The \(\pi\) number estimation. 1 Further investigation led me to the Monte Carlo method page of Wikipedia 2 where I saw an example of approximating pi using this simulation. While becoming familiar with the design and operation of the detectors, and how total antineutrino flux could be obtained from such a small sample, I read about a simulation program called Monte Carlo. During full power operation, a reactor may produce 10 21 antineutrinos per second with approximately 100 per day being detected. Part 2 will introduce the infamous metropolis algorithm, and Part 3 will be a specialized piece. This first tutorial will teach you how to do a basic crude Monte Carlo, and it will teach you how to use importance sampling to increase precision. During the summer of 2012, I had the opportunity to participate in a research experience for teachers at the center for sustainable energy at Notre Dame University (RET cSEND) working with Professor John LoSecco on the problem of using antineutrino detection to accurately determine the fuel makeup and operating power of nuclear reactors. This is the first of a three part series on learning to do Monte Carlo simulations with Python.
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