Convergence of the Binomial Distribution

Implemented in Mathematica by Jay Pottharst

Unscaled:

Scaled:

Module[{l, cut}, Manipulate[
ListPlot[
 If[scaled, cut = .01 Binomial[n, Floor[n/2]]];
 l = Select[
   Table[{n, k, Binomial[n, k]}, {k, 0, n}],
   If[scaled, (#[[3]] > cut) &, True &]
 ] /. {n_Integer, k_, b_} :>
   Tooltip[{k, b},
    TraditionalForm@SequenceForm[HoldForm@Binomial[n, k], " = ", b]],
 PlotMarkers -> Automatic,
 Joined -> True,
 Filling -> Axis,
 PlotRange -> All,
 AxesOrigin -> l[[1, 1]],
 AxesLabel -> {"k", TraditionalForm[Binomial["n", "k"]]},
 ImageSize -> Large],
{{n, 2}, 1, 1000, 1},
{scaled, {False, True}}
]]