% This code generates a single frame of the above animation.  % 10 frames are generated and put together to create the gif animation. function densityEstimation  N = 100; d = 3; pp = 0.4;  % Mixture ratio p = rand(N, 1) > pp;  % 1) Plot the Actual density x = -4:0.01:6.5; y = (1-pp)*normpdf(x,0,1) + pp*normpdf(x,d,1); plot(x, y, 'LineWidth', 2.5)  % 2) Get samples from the density samp = genSamp(0, d, p); hold on stem(samp, 0.05*ones(size(samp)), 'r', 'LineWidth',1.5, 'MarkerSize', 6)  % 3) Put small Gaussian kernels around each sample lambda = 0.35; for i = 1:N     x = (samp(i)-3*lambda):0.01:(samp(i)+3*lambda);     y = normpdf(x,samp(i),lambda);     h = plot(x, 0.03*y, ':g', 'LineWidth',1.5);     set(h,'Color',0.5*[1,1,1]) end  % 4) Find the kernel density estimate x = -4:0.01:6.5; y = zeros(size(x)); for i = 1:N     y = y + normpdf(x,samp(i),lambda); end y = y/N; plot(x, y, '--k', 'LineWidth', 2.5)  % Format axes set(gca,'LineWidth',2, 'FontSize', 20) axis([-4 8 0 0.3])  end  function samp = genSamp(x1, x2, p)  samp = p.*(x1+ randn(length(p), 1)) + (1-p).*(x2+ randn(length(p), 1)); end