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(Monte Carlo Integration) The average value of a function f over an interval [a, b] is given by Savg = -a f(2) dr. This formula can be used to approximate an integral by approximating the average value of ƒ by sampling the value of f(x) at a large number of randomly chosen points in [a, b] and computing the sample mean of these values. That is, f(r) dx = N i=1

(Monte Carlo Integration) The average value of a function f over an interval [a, b] is given by Savg = -a f(2) dr. This formula can be used to approximate an integral by approximating the average value of ƒ by sampling the value of f(x) at a large number of randomly chosen points in [a, b] and computing the sample mean of these values. That is, f(r) dx = N i=1

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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(Monte Carlo Integration) The average value of a function f over an interval [a, b] is given by 1 favg = f(2) dz. b - a This formula can be used to approximate an integral by approximating the average value of ƒ by sampling the value of f(x) at a large number of randomly chosen points in [a, b] and computing the sample mean of these values. That is, N [ f(x) dz = N i=1 where the r; are chosen randomly according to a uniform distribution in the interval [a, b]. Note: While this idea is actually inefficient in 1 dimension, it is a common strategy for very high dimensional integrals and there are numerous improvements that can be made to make it even mroe efficient. mc_int Function: Input variables: • an anonymous function representing f • a scalar representing a • a scalar representing b • a scalar representing N Output variables: a scalar representing the value of the integral A possible sample case is: >> approx_int approx_int = 0.99821 mc_int(@(x) sin(x), 0, pi/2, 1000) %3D
Transcribed Image Text:(Monte Carlo Integration) The average value of a function f over an interval [a, b] is given by 1 favg = f(2) dz. b - a This formula can be used to approximate an integral by approximating the average value of ƒ by sampling the value of f(x) at a large number of randomly chosen points in [a, b] and computing the sample mean of these values. That is, N [ f(x) dz = N i=1 where the r; are chosen randomly according to a uniform distribution in the interval [a, b]. Note: While this idea is actually inefficient in 1 dimension, it is a common strategy for very high dimensional integrals and there are numerous improvements that can be made to make it even mroe efficient. mc_int Function: Input variables: • an anonymous function representing f • a scalar representing a • a scalar representing b • a scalar representing N Output variables: a scalar representing the value of the integral A possible sample case is: >> approx_int approx_int = 0.99821 mc_int(@(x) sin(x), 0, pi/2, 1000) %3D
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