You might like to experiment with the bivariate normal. Here is the Mathematica code that I used to plot the joint density function. You can copy and paste this code into Mathematica and they play with viewing from different angles or changing the value of the correlation, r.

S = ParallelTable[ Plot3D[PDF[ MultinormalDistribution[{1, 1}, {{1, r }, {r , 1}}], {x, y}], {x, -3, 4}, {y, -3, 4}, PlotRange -> All, MeshFunctions -> {#3 &}, PlotPoints -> 50], {r, {0, 0.6}}]