I think OP just kind of enjoys these little simulations. It’s rewarding (to some) to see mathematical predictions actually work out. As a probability nerd myse

I think OP just kind of enjoys these little simulations. It’s rewarding (to some) to see mathematical predictions actually work out. As a probability nerd myself, I was yelling at my browser for him to take the difference between the true CDF and the empirical CDF. I.e., not just the plot where “analysis” CDF overlaps empirical CDF, but the difference between the two, scaled up by some number…say, the square root of the number of samples? ;-) Then we would have a realization of a discretized Brownian bridge, a kind of rescaled Brownian motion. And then we could have all kinds of fun looking at where the maximum difference falls (it will usually not be near the endpoints), and the size of the set adjacent to the maximum, and the local behavior of the process around the maximum (it’s expectation should be “cusped”, not smooth, although other processes will be smooth there). Some of those topics are really rather advanced, and they are all accessible by simulation if you follow your nose.