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    %% Maximum Likelihood Estimation
%

% Copyright 2015 The MathWorks, Inc.


%% Distribution of Sample Means
mu = 1; % Population parameter
n = 1e3; % Sample size
ns = 1e4; % Number of samples

rng default  % For reproducibility
samples = exprnd(mu,n,ns); % Population samples
means = mean(samples); % Sample means


%% Fit a Normal Distribution to Sample Means
[muhat,sigmahat,muci,sigmaci] = normfit(means)


%% Plot Histogram of Sample Means
numbins = 50;
histogram(means,numbins)
hold on
[bincounts,binpositions] = hist(means,numbins);
binwidth = binpositions(2) - binpositions(1);
histarea = binwidth*sum(bincounts);
x = binpositions(1):0.001:binpositions(end);
y = normpdf(x,muhat,sigmahat);
plot(x,histarea*y,'r','LineWidth',2)