Gaussians? Why Gaussians? Why not Cauchy for example (it has fatter tail)? And why identity matrix for the Gaussian covariance?
I really like the way you are using your technical skills for computation but I think you are using it on the wrong problem.
In reality, even if your dart throws are Gaussians they need not be independent of each other.
I'm coming from math background and was observing math people(physicists as a proxy) to the approach of making unreasonable assumptions if they will simplify the problem and make it solvable.
It reminds me of the joke:
A person is walking around a street light. Another asks him
I really like the way you are using your technical skills for computation but I think you are using it on the wrong problem.
In reality, even if your dart throws are Gaussians they need not be independent of each other.
I'm coming from math background and was observing math people(physicists as a proxy) to the approach of making unreasonable assumptions if they will simplify the problem and make it solvable.
It reminds me of the joke:
A person is walking around a street light. Another asks him
"What are you doing there?"
"Looking for my keys."
"Did you lose them there?"
"No, but there is more light here."
Edit: formatting