Suppose $ X_1,X_2,…$ are Bernoulli random variables with $ P(X_i=1)=p_i$ and $ X_i$ have negative correlation. Is there a CLT in this case, i.e. does $ \frac{Z_n-(\Sigma^n_{i=1}p_i)}{\sqrt{n}}$ converge to a Gaussian in distribution? And if we add the assumption that $ \underset{n \longrightarrow \infty}{lim} \frac{\Sigma^n_{i=1}p_i}{n}=p\in(0,1)$ , is it true then?Read more