%Problem Set 7 Due Wednesday Oct. 17, 2007

close all; %closes all figures
clc; %clears the screen
clear; %clears the memory

%set the normal and unit density seeds
randn('seed',1234);
rand('seed',0);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%2. a.
%m x n matrix 
%note that in our homework it says length "n" but to retain standard
%matrix notation we use length "m" of a matrix

%m is a 6 x 1
m = [5, 10, 30, 100, 500, 1000];
n = 10000;
dof = 3; 

figure;
for i = 1:1:6
    %generate the random draws
    x = trnd(dof,m(1,i),n);
    xbar = mean(x)';

    %plot the vector
    subplot(4,6,i);
    plot(xbar,'k');
    axis([0 n -6 6]);

    %plot the histogram
    subplot(4,6,i+6);
    edges = [-4:0.05:4];
    hist(xbar,edges);

    %plot the histogram of standardized means
    ybar = xbar./[std(x)'/sqrt(m(1,i))];
    subplot(4,6,i+12);
    hist(ybar);
    axis([-10 10 0 7500]);
    set(gca, 'Xtick', [-10 0 10]);

    %smoothed the histrogram distribution using Gaussian Kernel density estimator
    [ybarsmooth, domain] = kernel(ybar);
    subplot(4,6,i+18);
    plot(domain,ybarsmooth,'k');
    %plot(ybarsmooth,'k');
    axis([-10 10 0 0.5]);
end