Self-study note: Multivariate Analysis with Mathmatica. (Multinomial distribution)

multinomial1.m

n = 10;
p1 = 0.3;
p2 = 0.4;
ListPointPlot3D[
 Table[
  (
    Factorial[n] /(Factorial[y1]*Factorial[y2]*Factorial[n - y1 - y2])
    ) * p1^y1* p2^y2* (1 - p1 - p2)^(n - y1 - y2),
  {y1, 0, n},
  {y2, 0, n}
  ],
 Filling -> Axis,
 PlotRange -> All,
 FillingStyle -> Thickness[0.008]
 ]

multinomial2.m

r = 0.5;
Plot3D[
 PDF[
  BinormalDistribution[
   {0, 0}, {1, 1}, r
   ], {x, y}
  ], {x, -3, 3}, {y, -3, 3}, PlotRange -> All
 ]