Suppose (y_{i}=sum_{j=1}^{n_{i}} y_{i j}), where (y_{i j} sim operatorname{Bernoulli}left(p_{i} ight)) and are positively correlated with (operatorname{cor}left(y_{i j},

Suppose \(y_{i}=\sum_{j=1}^{n_{i}} y_{i j}\), where \(y_{i j} \sim \operatorname{Bernoulli}\left(p_{i}\right)\) and are positively correlated with \(\operatorname{cor}\left(y_{i j}, y_{i k}\right)=\alpha>0\) for \(k eq j\). Prove \(\operatorname{Var}\left(y_{i}\right)>n_{i} p_{i}\left(1-p_{i}\right)\).