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<HTML><HEAD><TITLE>Exponentially Distributed Random Variables</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="tex2html6592" HREF="page472.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6590" HREF="page468.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6586" HREF="page470.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html6594" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0014523000000000000000">Exponentially Distributed Random Variables</A></H3><P>Program <A HREF="page471.html#progexponentialRVa"><IMG ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A> defines the <tt>ExponentialRV</tt> class.This class generates exponentially distributed random numbers with a mean value of <IMG WIDTH=9 HEIGHT=16 ALIGN=MIDDLE ALT="tex2html_wrap_inline68653" SRC="img1928.gif" >.The mean value <IMG WIDTH=9 HEIGHT=16 ALIGN=MIDDLE ALT="tex2html_wrap_inline68653" SRC="img1928.gif" > is specified in the <tt>__init__</tt> method.<P><P><A NAME="34002"> </A><A NAME="progexponentialRVa"> </A> <IMG WIDTH=575 HEIGHT=145 ALIGN=BOTTOM ALT="program33916" SRC="img1929.gif" ><BR><STRONG>Program:</STRONG> <tt>ExponentialRV</tt> class.<BR><P><P>The <tt>ExponentialRV</tt> class generates a sequence of random numbers, <IMG WIDTH=17 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline68657" SRC="img1930.gif" >,<em>exponentially distributed</em><A NAME=33929> </A>on the interval <IMG WIDTH=42 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline68659" SRC="img1931.gif" > and having a mean value <IMG WIDTH=9 HEIGHT=16 ALIGN=MIDDLE ALT="tex2html_wrap_inline68653" SRC="img1928.gif" >.The numbers are said to be <em>exponentially distributed</em> becausethe probability that <IMG WIDTH=17 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline68657" SRC="img1930.gif" > falls between 0 and <I>z</I> is given by<P> <IMG WIDTH=348 HEIGHT=37 ALIGN=BOTTOM ALT="displaymath68651" SRC="img1932.gif" ><P>where <IMG WIDTH=102 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline68669" SRC="img1933.gif" >.The function <I>p</I>(<I>x</I>) is called the<em>probability density function</em><A NAME=33937> </A>.Thus,<P> <IMG WIDTH=500 HEIGHT=58 ALIGN=BOTTOM ALT="eqnarray33938" SRC="img1934.gif" ><P>Notice that <IMG WIDTH=97 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline68673" SRC="img1935.gif" > is a value between zero and one.Therefore, given a random variable, <IMG WIDTH=14 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline68643" SRC="img1925.gif" >,uniformly distributed between zero and one,we can obtain an exponentially distributed variable <IMG WIDTH=17 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline68657" SRC="img1930.gif" > as follows:<P><A NAME="eqnalgsedrv"> </A> <IMG WIDTH=500 HEIGHT=43 ALIGN=BOTTOM ALT="eqnarray33946" SRC="img1936.gif" ><P>Note, if <IMG WIDTH=14 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline68643" SRC="img1925.gif" > is uniformly distributed on (<I>O</I>,1),then so too is <IMG WIDTH=15 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline68683" SRC="img1937.gif" >.The implementation of the <tt>next</tt> methodfollows directly from Equation <A HREF="page471.html#eqnalgsedrv"><IMG ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>.<P><HR><A NAME="tex2html6592" HREF="page472.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6590" HREF="page468.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6586" HREF="page470.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html6594" 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 © 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a> All rights reserved.</ADDRESS></BODY></HTML>⌨️ 快捷键说明
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