I've made a 2D walker to compare different RNG's. I'm measuring the succes of each walk as the distance from the origin to the endpoint, using the regular 2-norm. The thing I can't seem to work out is the variance.
D_n=\sqrt(x_n^2+y_n^2)
Var(D_n)=E[D_n^2]=E[Z_1^2+...+Z_n^2]
Since...