Quit[]

B[n_,p_,k_]:=PDF[BinomialDistribution[n,p],k];
poisson[λ_,k_]:=PDF[PoissonDistribution[λ],k];
normal[μ_,σ_,x_]:=PDF[NormalDistribution[μ,σ],x];

n1=100;p1=0.01;
n2=50;p2=0.01;
n3=50;p3=0.1;
n4=100;p4=0.1;
n5=4;p5=0.9;
n=n5;p=p5;
λ=n*p
kmax=10*λ;
table1=Table[{k,B[n,p,k]},{k,0,kmax}];
table2=Table[{k,poisson[λ,k]},{k,0,kmax}];
pl1=ListPlot[table1,PlotStyle->RGBColor[1,0,0],Joined->True,PlotRange->{0,0.6}];
pl2=ListPlot[table2,PlotStyle->{PointSize[0.02],RGBColor[0,0,0]}];
Show[pl1,pl2]

λ=1.0;
n1=100; n2=50; n3=10; n4=5;n5=3;
n=n3;p=λ/n;
kmax=10*λ;
table1=Table[{k,B[n,p,k]},{k,0,kmax}];
table2=Table[{k,poisson[λ,k]},{k,0,kmax}];
pl1=ListPlot[table1,PlotStyle->RGBColor[1,0,0],Joined->True];
pl2=ListPlot[table2,PlotStyle->{PointSize[0.02],RGBColor[0,0,0]}];
Show[pl1,pl2]

n=4000;
μ=5;σ=3;
data=RandomVariate[NormalDistribution[μ,σ],n];
dist=Plot[PDF[NormalDistribution[μ,σ],x],{x,-7,15},PlotStyle->Thick];
hist=Histogram[data,80,"ProbabilityDensity"];
Show[dist,hist]

n=200;p=0.3;
μ=n*p;σ=Sqrt[n*p*(1-p)]
dist=DiscretePlot[PDF[BinomialDistribution[n,p],k],{k,0,n},PlotStyle->{RGBColor[1,0,0];PointSize[0.02]},PlotRange->{0,0.08}];
dist1=Plot[PDF[NormalDistribution[μ,σ],x],{x,μ-2*σ,μ+2*σ},PlotStyle->Thick];
hist=Histogram[data,n,"ProbabilityDensity"];
Show[dist,dist1]

dist=DiscretePlot[PDF[BinomialDistribution[n,p],k],{k,0,n},PlotStyle->{}]

Sqrt[6./7.]

0.8220*2-1

(29.5-35)/Sqrt[35*10/12]