Re: Limiting Distribution
First, let's find the distribution of 
, this can be done by computing the characteristic function  = \displaystyle \phi_{\frac{1}{n}\sum_{i=1}^{n}}(t)=\phi_{\sum_{i= 1}^{n }X_i}\left(\frac{t}{n}\right))
and because 
we have given that )
are independent random variables we obtain  = \prod_{i=1}^{n} \phi_{X_i}\left(\frac{t}{n}\right))
. 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  = P(W_n \leq x))
. Can you compute this?
be independent Bernoulli(
) random variables and let
. Find the limitiing distribution of
