function xcheby(X, pf, k) 
% xcheby(X, pf, k)  Analyzes the Weak Law of Large Numbers using the 
%    Chebyshev bound.  The output is the number of times the sample mean 
%    of each experiment in X was k standard deviations away from the  
%    population mean.  pf is X's associated probability function. 
if ispf(pf)==0 
   error('invalid probability function') 
end 
s=size(X); 
hit=sum(inrange(rvmean(X), mmean(pf), k*var(pf)/sqrt(s(2)))); 
S=sprintf('Experimental mean fell outside %.4f variances', k); 
disp(S); 
miss=(s(1)-hit)/s(1); 
S=sprintf('%d of %d times - %1.4f', s(1)-hit, s(1), miss); 
disp(S); 
S=sprintf('Chebyshev bound - %1.4f', 1/k); 
disp(S);