function homework_example
%HOMEWORK_EXAMPLE Example MATLAB function for LaTeX homework templates.
%  This function produces a figure by using a number of MATLAB commands. It
%  should help generate the power of the \matlabscript macro for including
%  MATLAB functions and scripts within code.
%
%  The figure generated by this function will be used to demonstrate how to
%  use \scalefig.

% Generate 100 random data points with a normal distribution
X = randn(1, 100);

% Generate a histogram in N at 100 centers specified at Xcenters
[N, Xcenters] = hist(X, length(X)/10);

% Plot the sample CDF of the data
clf;
subplot(211);
cdf_datafig = stairs( sort(X), linspace(0,1,length(X)) );

% Plot an expected CDF on top of it
hold on;
xlims = xlim;
expX = linspace(xlims(1), xlims(2), 1000);
cdf_expfig = plot( expX, normcdf(expX), 'r--' ); 

% Label the figure
legend( [cdf_datafig, cdf_expfig], 'Data Distribution', ...
                                   'Expected Distribution', 4 );
xlabel('x');
ylabel('F(x) = P(X \leq x)');
title('Normal Cummulative Distribution Function');

%%% Notice the use of TeX in the above ylabel. In MATLAB 7.0, LaTeX can
%%% also be used if the interpreter on the text object is changed from
%%% 'tex" to 'latex'. 

% Plot the sample pdf of the data
subplot(212);
pdf_datafig = bar( Xcenters, N/length(X)/(Xcenters(2)-Xcenters(1)) );
xlim( xlims );

% Plot an expected pdf on top of it
hold on;
pdf_expfig = plot( expX, normpdf(expX), 'r--' );

% Label the figure
legend( [pdf_datafig, pdf_expfig], 'Data Density', ...
                                   'Expected Density', 1 );
xlabel('x');
ylabel('dF(x)/dx');
title('Normal Probability Density Function');