:= expectation 𝔼 [f( X ⏟ ∼ 𝒰 ([0,1]d) )] = integral ∫ [0,1]d f(x) dx ≈ sample mean 1 n n ∑ i=1 f(xi ) =: ̂ μn Fill space better better than grids 0.00 0.25 0.50 0.75 1.00 xi1 0.00 0.25 0.50 0.75 1.00 xi2 0.00 0.25 0.50 0.75 1.00 xi1 0.00 0.25 0.50 0.75 1.00 xi3 0.00 0.25 0.50 0.75 1.00 xi1 0.00 0.25 0.50 0.75 1.00 xi4 64 Independent and identically distributed (IID) points, (d = 6)