clc;
close all;
clear all;
%where you put the lnnormlike.m file
addpath('U:\Public\html\files\matlab\functions');

m = 500;
n = 1;    
mu = 2;
sigma2 = 2;

%initialize our matrices (fill them with 999 so we can easily see if the
%values are replaced).
xbarvec = 999*ones(100,1);
s2vec = 999*ones(100,1);
thetamat = 999*ones(100,2);

for i = 1:1:100
%don't set a seed. doing so will give the same answer in each loop.
x = normrnd(mu,sqrt(sigma2),m,n);
xbarvec(i,1) = mean(x,1);
s2vec(i,1) = sum((x-mean(x,1)).^2)/m;

x0 = [1.95, 2.05]; %initial guess for the minsearch function
%returns the MLE estimates of mu and sigma^2 in a 2x1 matrix
theta5g = fminsearch(@(theta) lnnormlike(theta,x), x0);
%save the estimates of each loop in a matrix
thetamat(i,1:2) = theta5g; 

end;

%average our numerical estimates
meanxbarvec = mean(xbarvec);
means2vec = mean(s2vec);
meanthetamat = mean(thetamat);

%calculate the variance of our numerical estimates
varxbarvec = var(xbarvec);
vars2vec = var(s2vec);
varthetamat = var(thetamat);