Let random variable X = Y1+Y2+.....Yn. are iid rvs. We have to Generate Binomial(n,p) rv X. For this first, we have to generate Bernoulli rvs {Yi's} with mean p. Then we have to find X = Summation(Yi's) (summation is sigma from 1 to n). Then it will give us Binomial rv with parameters n and p. we have to plot the pdf and cdf of this result.
Can anybody help me to solve this?
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How to generate a Binomial random variable by using Bernoulli random variables? The idea is: (i) Generate Bernoulli random variables Yi's with mean p (ii) Set X = sum(Yi's).
This will give us a Binomial random variable with parameters n and p. (Convolution method). How to do this in MATLAB
Answers (2)
Adam Danz
on 21 Aug 2018
Edited: Adam Danz
on 21 Aug 2018
Does this help?
p=0.3;
n = 100000;
b=(rand(1,n)<p);
%test it
mean(b)
2 Comments
Adam Danz
on 22 Aug 2018
I'm not sure what you mean. I don't know what this means: " Set X = sum(Yi's)."
If you want " a Binomial random variable with parameters n and p", then that's what I showed you. If you want to sum them,
x = sum(b)
It's not clear conceptually what you're looking for.
Torsten
on 22 Aug 2018
Edited: Torsten
on 22 Aug 2018
p = 0.3;
n = 25;
nsample_binomial = 1000000;
for i = 1:nsample_binomial
bernoulli = (rand(1,n)<=p);
binomial(i) = sum(bernoulli);
end
%Test for mean and variance
mean(binomial)-n*p
var(binomial)-n*p*(1-p)
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