\begin{equation} \label{eq:var_tilde_psi_eq_3}
	\frac{\delta}{6} \left( 1-\sum_{i=0}^k {4N+1 \choose i} \alpha^i (1-\alpha)^{4N+1-i} \right) =  \left(1+\frac{\delta}{6N}\right) N {N \choose k} \alpha^{k+1} (1-\alpha)^{N-k},
\end{equation}
