function bias = cmpt_ml_var_bias(N_MC)
% CMPT_ML_VAR_BIAS - studies the bias in the MaxLikelihood estimate of the variance
%
% Input: 
%   N_MC: the number of monte carlo estimates to do of the following procedure
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

% generate N_SAMPS ramdom samples:
N_SAMPS=10; 

data = randn(N_SAMPS,N_MC); 

%mu = mean(data);
%sigma_hat_sq = mean( ( data - repmat(mu,N_SAMPS,1) ).^2 ); 
sigma_hat_sq = var(data,1);    % <- computed using a biased estimator 
%sigma_hat_sq = var(data);     % <- computed using an unbiased estimator 

% take the mean of all of these samples (and compute the bias):
bias = mean(sigma_hat_sq) - 1;