# Sum of Bernoulli random variables

*From*: swk.aio@xxxxxxxxx*Date*: Tue, 27 May 2008 01:58:32 -0700 (PDT)

Hello,

Suppose S = X_1 + X_2 + ... + X_n where X_i is a 0-1 random variable

with Pr(X_i = 1) = p_i and Pr(X_i = 0) = 1-p_i.

If all the p_i are the same, it is just a binomial random variable.

However, can we say anything when the p_i are not the same?

Furthermore, what will it be if p_i are also random variables with

some distribution?

I did some simulation and it seems that the sum of the Bernoulli

random variables with different p_i looks like a normal distribution.

Thanks,

Peter

.

**Follow-Ups**:**Re: Sum of Bernoulli random variables***From:*illywhacker

**Re: Sum of Bernoulli random variables***From:*Richard Ulrich

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