% Sum of independent RVs demo
% 
%  Brian D. Jeffs 10/26/05

echo on
x = [-1.1:.001:1.1];

f_X = 1/2*(abs(x) <= 1);

plot(x, f_X)
a = axis;
axis(1.1*a);
title('pdf for X ~ U(-1,1)');
xlabel('x');
ylabel('f_X(x)');
pause

f_Y = f_X;
y = x;
N = 1;
again = 1;
while again
    
    N = N + 1;
    
    f_Y = conv(f_Y, f_X)./1000;
    
    y = [min(y)-1.1:.001:max(y)+1.1]';
    
    f_Gauss = normpdf(y, 0, 2*N/12);
    plot(y, f_Y(1:length(y)), y, f_Gauss)
    a = axis;
    axis(1.1*a);
    title(['pdf for f_X * f_X(x) * ... ',num2str(N),' times']);
    xlabel('y');
    ylabel('f_Y(y)');
    legend('Sequence of convolved unforms','Gaussian with matching variance')
    again = input('Convolve f_Y with f_X again? (1/0): ');
end
echo off