Before revision:  Formally, we show that for any \varepsilon, there exists a constant C_{\varepsilon = poly(1/\varepsilon) (independent of n)such that after removing C_{\varepsilon} distributions of our choice, we can achieve a (\beta - \varepsilon)-approximation to the resulting maximum.
After revision:  - We show that for any \varepsilon, there exists a constant C_{\varepsilon = poly(1/\varepsilon) (independent of n)such that after removing C_{\varepsilon} distributions of our choice, we can achieve a (\beta - \varepsilon)-approximation to the resulting maximum.