Let be independent Bernoulli( ) random variables and let . Find the limitiing distribution of
First, let's find the distribution of , this can be done by computing the characteristic function and because we have given that are independent random variables we obtain . Now, the only thing you have to do is calculating the characteristic function of a random variable with a Bernoulli distribution. Can you do that?
Second, we want the distribution of , in fact we want to find the distribution function . Can you compute this?