1. ## bernoulli

If X_1, X_2,.... X_n are Bernouilli independent random variables, how is it possible to approximate the distribution of P= Sum of X_i / n ?

What does it mean? What is it asking?

2. Originally Posted by 0123
If X_1, X_2,.... X_n are Bernouilli independent random variables, how is it possible to approximate the distribution of P= Sum of X_i / n ?

What does it mean? What is it asking?
Bernoulli distributions can be approximated using Binomial distributions which in turn can be approximated by Poisson distributions provided the number of trials is large and the probability of success is small.

3. Originally Posted by Jhevon
Bernoulli distributions can be approximated using Binomial distributions which in turn can be approximated by Poisson distributions provided the number of trials is large and the probability of success is small.
I know that binomial can be approximated by normal distribution when n is large. What is the right answer? and why? Thank you