%stat351 stat351-histogram.m
%Histograms and empirical distributions
>>X=exprnd(1,10000,1);

%[N,X] = HIST(...) also returns the position of the bin centers in C.
>>[N,C]= hist(X,10) 

>>N'
ans =
        5946
        2351
        1007
         420
         173
          60
          23
          14
           4
           2
>>C'
ans =

    0.4619
    1.3857
    2.3094
    3.2332
    4.1569
    5.0807
    6.0045
    6.9282
    7.8520
    8.7757
    
%sample freqency

>>f= N'/10000
f =

    0.6054
    0.2419
    0.0930
    0.0339
    0.0154
    0.0062
    0.0018
    0.0017
    0.0002
    0.0005

>>sum(f)

ans =

    1.0000
        
%E(X)

C'.*f

>>sum(C'.*f)
ans = 
       1.0633

%Simulation 
X=unifrnd(0,1,10,10000);
    
>> size(X)

ans =

       10          10000
>> help max

 MAX    Largest component.
    For vectors, MAX(X) is the largest element in X. For matrices,
    MAX(X) is a row vector containing the maximum element from each
    column.
    
 >>X_n =max(X);
>> size(X_n)       

ans =

           1       10000
[N,C]=hist(X_n,10);

f=N'/10000;
>> plot(C',f,'-')