Here is another piece of code "to analyse" the density of the points obtained, using the assumption that the density is something like Exp[ - a x^2 ]
xx = RandomReal[NormalDistribution[0, .3], 500];
yy = RandomReal[NormalDistribution[0, .3], 500];
pp2 = Transpose[{xx, yy}];
ListPlot[pp2, AspectRatio -> Automatic,
PlotRange -> {{-1, 1}, {-1, 1}}, PlotStyle -> {Red, Blue}]
total = Length [pp2]; pts =
Table[{d + .05,
N@Length[Select[pp2, d < Sqrt[#.#] < d + .1 &]]/total}, {d, 0,
2, .1}]
fit = NonlinearModelFit[pts,
2 Pi x b Exp[-a x^2], {{b, .21}, {a, 6.2},}, x];
ffit = Normal[fit]
Plot[ffit, {x, 0, 2}, PlotRange -> {0, .3}, Epilog -> Point /@ pts]
Run this code several times and look at the plots