Let $U, V$ be two standard normal random variables with covariance $cov(U,V) = \beta \in [0,1)$. Let $W = UV$ be the product of two RV's, and $W_1, W_2, \ldots, W_n$ be n i.i.d copies of $W$, what's the tail bound for $Y = \frac{1}{n}\sum_{i=1}^nW_i - \beta$? That is, for any $t > 0$, $P(Y < -t) < ?$ and $P(Y > t) < ?$.