Homepage › Solution manuals › Gilbert Strang › Linear Algebra and Learning from Data › Exercise 5.1.8
σ2 = ∑ pi(xi−m)2 = ∑ pi(xi2−2mxi+m2) = ∑ pixi2−2m∑ pixi+m2 ∑ pi = ∑ pixi2−2m2+m2 = ∑ pixi2−m2