Can anybody help me to solve this?

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

[ASWATHI V]

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.

Answer 1

[Adam Danz]

Does this help?

p=0.3;
n = 100000; 
b=(rand(1,n)<p);

%test it

mean(b)

[ASWATHI V]

Is it similar to summation? We have to summed up 'n' Bernoulli random variables.

[Adam Danz]

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.

Answer 2

[Torsten]

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)

[ASWATHI V]

Thank you. How can I plot the CDF and PDF of binomial using this?

[Walter Roberson]

Without a loop:

p = 0.3;
n = 25;
nsample_binomial = 1000000;
binomial = sum(rand(n, nsample_binomial) <= p);

For computing and plotting cdf, see https://www.mathworks.com/matlabcentral/answers/24299-computing-cdf#answer_322552

[ASWATHI V]

But when I am plotting CDF and PDF it is not coming in the same way as we need. We cant use cdfplot for plotting CDF, First we have to plot the PDF and from that the CDF. But its not getting.

[Walter Roberson]

Shrug. We do not know exactly what plots you need.

https://www.mathworks.com/matlabcentral/fileexchange/19121-probability-density-function-pdf-estimator-v3-2