Plotting the mean and variance of 100 Brownian/Wiener paths

I'm trying to plot the mean of 100 Brownian paths. I have the Brownian script correct, but when I try plotting the mean and variance, it's giving me the whole 100 paths instead of just one for the mean. This is my code. Thank you.

figure; hold on; grid on;
for i = 1:100
  W(:,i) = brownianPath(1,200);
  l1 = mean(W,2);
  l2 = var(W,2);
  plot(l1,'g-');
end

Answer 1

[John D'Errico]

Computing the mean INSIDE the loop is wrong.

If you will compute the paths in a loop, wait until after the loop to compute the mean and variance. So perhaps this might be closer to what you wanted to see:

figure; hold on; grid on;
for i = 1:100
  W(:,i) = brownianPath(1,200);
end
l1 = mean(W,2);
l2 = var(W,2);
plot(l1,'g-');

[Mel Hernandez]

Thank you so much!