%%% Examples of Large N Approximations
clc
format compact
format short g
% Stirling's Formula
n=[1:10,20:10:100];
fact=factorial(n);
approx1 = (n/exp(1)).^(n).*sqrt(n);
approx2 = (n/exp(1)).^n.*sqrt(2*pi*n);
error1= abs(fact-approx2)./fact*100;
[n;fact;approx1;approx2; error1]'

% Binomial v. Poisson
n=1000
p=0.004
l=4
k=0:1:10;
list1=[n:-1:n-10+1];
list2=[1:10];
bcoeffs=[1, cumprod(list1)./cumprod(list2)];
binom=bcoeffs.*p.^k.*(1-p).^(n-k);
poisson=exp(-4)*4.^k./factorial(k);
[k;binom;poisson]'