%% Monte carlo project 2
N = 1;
n=10000;
test = zeros(N+1, 2*n);


for j=1:N
r = rand(1,n);
test(j+1, :) = test(j, :) + draw(r);
end
%%

saw = 0;
for j = 1:length(test)-1
if(size(unique(test(:, j:j+1), 'rows')) == size(test))
    saw=saw+1;

end
end
saw

%%
r = linspace(0,N,100000);
gdist = @(x, n) 2*x.*exp(-x.^2/n)/n; %x equals radius, which represents which is max n in our case;

plot(r, gdist(r, 6))
%%
subplot(211)

histogram(radius)
subplot(212)
plot(r, gdist(r, 10))

%%