Manipulate[
ListPlot[
Table[
{k,E^(-lambda)lambda^k/k!}, 
{k,0,50}
], 
PlotRange->{0,.5}
],
{lambda,1,50}
]

Histogram[Table[RandomInteger[PoissonDistribution[20]], {100000}],Automatic,"PDF",Epilog->First@ListPlot[Table[{x+.5,PDF[PoissonDistribution[20],x]},{x,0,40}],PlotStyle->Red]]