1) Bar Histogram review
 - xn measurements from finite list xk (e.g., 0,1,2,3,... or 10,20,...) 
 - Nk number of times xk occurred
 - N=sum(Nk); % total number of measurements
 - Fk=Nk/N;   % fractional distribution
 - sum(Fk)=1  % Normalized
 - mean(xn)=sum(xn)/N=sum(Fk.*xk); % exact
 - var(xn)=sum((xn-mean(x)).^2)/(N-1)=sum(Fk.*(xk-mean(xn)).^2)/(N-1) % exact
2) Bin Histogram review
 - xn measurements from continuous binned list dxk (e.g., 0-1,1-2,2-3,...) 
 - Nk number of times xn was in the range dxk
 - N=sum(Nk);       % total number of measurements
 - Fk=Nk/N=fk*dxk;  % definition of fk (fk*dxk fraction in bin dxk)
 - fk*dxk = \int_{xk}^{xk+dxk) f(x)dx; % relation to limiting or ideal dist.
 - sum(fk*dxk)=1;  % normalized
 - mean(xn)=sum(xn)/N~=sum(xk.*fk*dxk); % approx exact as N->inf
 - var(xn)=sum((xn-mean(x)).^2)/(N-1)~=sum((xk-mean(xn)).^2.*fk*dxk)% approx
3) Limiting and ideal
 - X infinite number of measurements from infinitesimal bins dx
 - f(x) (P)robability (D)ensity (F)unction PDF
 - f(x)dx fraction of measurements in range [x,x+dx)
 - \int f(x)*dx=1; % normalize
 - fk*dxk=\int_{xk}^{xk+dxk) f(x)dx; % relation to limiting or ideal dist.
 - mean(X)=\int x*f(x)*dx
 - var(X)=\int (x-mean(X))^2*dx
 - if you let N->inf a bin histogram -> limiting distribution or PDF
 - ideal is a model limiting distribution
4) Normal distribution
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