λ=5;
τ=.5;
z=1-Exp[-λ τ];
expected[k_]:=Exp[-λ τ] (∑_(n=1)^k)(n (z^n));
data=Table[{k,expected[k]},{k,1,100}];
ListPlot[data,Joined->True,AxesOrigin->{0,0}]

pr[n_]:=(((1-Exp[-λ τ]))^n) Exp[-λ τ]
data=Table[{n,pr[n]},{n,0,100}];
ListPlot[data,Joined->True,AxesOrigin->{0,0},PlotRange->All,AxesLabel->{"n, number of\n cars passing\nbefore red light","P(X=n)"}]