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<HTML><HEAD><TITLE>Monte Carlo Methods</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html6603" HREF="page473.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6601" HREF="page464.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6595" HREF="page471.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6605" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H2><A NAME="SECTION0014530000000000000000">Monte Carlo Methods</A></H2><P>In this section we considera method for solving problems using random numbers.The method exploits the statistical properties of random numbersin order to ensure that the correct result is computedin the same way that a gambling casino sets the betting oddsin order to ensure that the ``house'' will always make a profit.For this reason,the problem solving technique is calleda <em>Monte Carlo method</em><A NAME=33954>&#160;</A>.<P>To solve a given problem using a Monte Carlo methodwe devise an experiment in such a waythat the solution to the original problem can be obtainedfrom the experimental results.The experiment typically consists of a series of random trials.A random number generator such as the one given in the preceding sectionis used to create the series of trials.<P>The accuracy of the final result usually dependson the number of trials conducted.That is, the accuracy usually increases with the number of trials.This trade-off between the accuracy of the resultand the time taken to compute itis an extremely useful characteristic of Monte Carlo methods.If only an approximate solution is required,then a Monte Carlo method can be very fast.<P><BR> <HR><UL> <LI> <A NAME="tex2html6606" HREF="page473.html#SECTION0014531000000000000000">Example-Computing  <IMG WIDTH=9 HEIGHT=7 ALIGN=BOTTOM ALT="tex2html_wrap_inline68687" SRC="img1938.gif"  ></A></UL><HR><A NAME="tex2html6603" HREF="page473.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6601" HREF="page464.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6595" HREF="page471.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6605" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright &#169; 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a>  All rights reserved.</ADDRESS></BODY></HTML>

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