Re: questions 5 & 6
All these are approximating integrals.
Many problems really are sums, but this one is, theoretically, continuous.
First you do 2D integrals to compute a, a 1D integral to compute bias,
and a 3D integral to compute variance.
(I think it would also work to compute bias+variance in the first place, and subtract bias to get variance, but I didn't try that.)
I used equally space points for all, but you could also use random points.
If I was in the right mood, I might have done Gaussian quadrature, or some other numerical integration method.
