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%使用Matlab來產生Bernoulli Random Variable序列之和的樣本空間 
%------------------------------MATLAB Script-------------------------------------- 
% file bernoulli_rvs 
% Sequence of Bernoulli Random variables 
% X_i are Bernoulli RVs with i=1,...,n 
n=input('Number of RVs='); 
m=input('Number of samples of the sum=');
 p=input('Parameter of Bernoulli RV='); 

%Sn=X_1+X_2+...+X_100 
B=rand(n,m)<=p; 
for i=1:m 
SUMOFBRV(i,1)=sum(B(:,i)); 
end k=[1:m]'; 
Samples=[k SUMOFBRV]; 
fprintf('\n\tSome samples of the sum of these %d Bernoulli RVs',n);
 fprintf('\n\t i \t S(i)\n'); 
disp(Samples); 
-------------------------------------------------------------------------- 
>> bernoulli_rvs Number of RVs n=100 
Number of samples of the sum m=10
Parameter of Bernoulli RV p=0.3 
>>
 random_sum 
Some samples of the sum of these 100 RVs
 i S(i) 
1 25 
2 34 
3 36
4 36 
5 36 
6 32 
7 32 
8 29 
9 31 
10 39 The probability density function of the sum of these n Bernoulli RVs can be approached by directly counting the number of relative frequencies of all possible numbers under a large number of trails. The following matlab program executes 100000 trials and counts the frequencies of all possible numbers. 
-------------------------------------MATLAB Script-------------------------------------
% pdf_of_the_sum.m 
n=input('Number of RVs n='); 
m=input('Number of samples of the sum m='); 
p=input('Parameter of Bernoulli RV p='); 
B=rand(n,m)<=p; 
for i=1:m 
SUMOFBRV(i,1)=sum(B(:,i)); 
end 
x=1:100; 
SEQ=hist(SUMOFBRV,x); 
SEQ1=SEQ/m; 
plot(x,SEQ1); 
xlabel('s') ylabel('pdf fS(s)') 
title('Probability density function of the sum of the 100 Bernoulli RVs') 
>> pdf_of_the_sum 
Number of RVs n=100 
Number of samples of the sum m=100000 
Parameter of Bernoulli RV p=0.3 
>>