MonteCarlo - Monte Carlo Estimation and Simulation James...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Monte Carlo Estimation and Simulation James Keesling In earlier sections of the course we have presented several ways to estimate integrals. These include, Newton-Cotes Closed and Newton-Cotes Open Formulas , Gaussian Quadra- ture , and Romberg Integration . In these methods we used exact algorithms and could cal- culate the error in the estimate in a precise way. The method we now introduce involves the random choice of points and a statistical estimate of the error. 1 Using Random Numbers to Estimate Integrals To start, we assume that we have a method for choosing points randomly from the unit interval so that the points come from a probability density function that is constant one on the interval. For practical purposes, the command rand () in your TI-89 will suffice. Suppose that we wish to estimate the integral R b a f ( x ) dx . The Monte Carlo Method does this by first choosing n random points from the unit interval [0 , 1]. Call this set of points { x i } n i =1 . Our formula for the estimate is given by the following calculation. b- a n n X i =1 f ( x i ) Think of the formula as calculating the average value of the function f ( x ) and multi- plying this value by the length of the interval [ a,b ]. The average value for the function is determined by a random sample of the points in the interval [ a,b ]. The term Monte Carlo was coined by Stanislaw Ulam for the process of using random numbers to make estimates...
View Full Document

This note was uploaded on 11/12/2011 for the course STA 3032 taught by Professor Kyung during the Summer '08 term at University of Florida.

Page1 / 3

MonteCarlo - Monte Carlo Estimation and Simulation James...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online