clear
trials=10000;
X=randn(trials,1)+4;

for i=1:trials
    while abs(X(i)-4)>2 
        X(i)=randn(1,1)+4;
    end
end
    


n=(1:100)/10;
pX=histc(X,n)/10; % Not really a pdf, just scaled to make the plot look good
hold off
figure(1)
bar(n,pX,'r')

y=(n-4).^2+10;

hold on
plot(n,y,'b')

yX=(X-4).^2+10;
number_of_bins=100;
bin_width=1/10;
n=8+(1:number_of_bins)*bin_width;
pY=histc(yX,n)/(trials*bin_width);
figure(2)
bar(n,pY,'r')

sum(pY*bin_width) %make sure it's a pdf, must sum to unity