%
% script to plot average of Cauchy random variables
% this to illustrate that the mean of a cauchy pdf
% does not converge and is undefined
%
% note: matlab has no pdf for cauchy, but it is the x/y where
% x,y are normal(0,1) random variables.
%
% Nasser Abbasi oct 20, 2007 for Math 502, CSUF
% 
close all;
randn('state',010101);
N = 1000;  %number of random variables to generate
s = 1:1:N; 
x = randn(N,1); %generate N normal r.v.
y = randn(N,1); %generate N normal r.v.
z = x./y;
av=cumsum(z)./s';
plot(s,av,'.','MarkerSize',5);
xlabel('Number of random variables');
ylabel('average of random variables');
title('Average of cauchy r.v. as function of N');