Sum of Bernoulli random variables



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
.



Relevant Pages

  • Re: Distribution of random sum of random variables
    ... N is a discrete nonnegative random variable ... >following random sum converges to the normal distribution? ... When EN is inifinite, the sum is ...
    (sci.math)
  • Re: Normal Random Variable Generator
    ... Excel, PowerPoint, and VBA add-ins, tutorials ... > random variables in Excel: ... > differ from a normal distribution. ... but I don't know how to use in my VBA code. ...
    (microsoft.public.excel.programming)
  • Re: Statistical Indep and Corr of Normal RVs
    ... uncorrelatedness implies independence is when the random variables ... Suppose two random variables X and Y are jointly normally ... has a multivariate normal distribution. ... "But ZERO correlation implies independence IF and ONLY IF the random ...
    (sci.stat.edu)
  • Re: jointly gaussian
    ... variables with normal distribution? ... if two random variables have a bivariate normal ... point leads me to suspect that you mean something else by the ... phrase "independent of each other" ...
    (comp.dsp)
  • Re: Distribution of random sum of random variables
    ... Eric Wong wrote: ... N is a discrete nonnegative random variable ... >following random sum converges to the normal distribution? ...
    (sci.math)