function xdirtbal(X, pf, m) 
% xdirtbal(X, pf, m) "dirtball statistics" for the random variable X.   
%    Generates a plot of the sample mean being trapped between the standard 
%    deviation of the associated probability function as the number of  
%    samples increases.  m is an optional parameter that specifies which 
%    experiment in the matrix X to use; if it is not specified, all 
%    experiments are used. 
if nargin==3 
   M=size(X); 
   if m<=0 | m>M(1) 
      error('invalid value for m') 
   end 
   X=X(m,:); 
else 
   X=X(:)'; 
end 
if ispf(pf)==0 
   error('not a valid probability function') 
end 
means=zeros(size(X)); 
ubounds=zeros(size(X)); 
lbounds=zeros(size(X)); 
V=var(pf); 
u=mmean(pf); 
U=ones(size(X)).*u; 
means(1)=X(1); 
ubounds(1)=u+V; 
lbounds(1)=u-V; 
for i=2:length(X), 
   means(i)=(means(i-1)*(i-1)+X(i))/i; 
   ubounds(i)=u+V/sqrt(i); 
   lbounds(i)=u-V/sqrt(i); 
end 
subplot(1,1,1); 
plot(ubounds); 
hold on 
plot(lbounds); 
plot(U, 'b'); 
plot(means, 'r'); 
hold off