\overline{W}) $ (with $w_i =\sharp W_i)$ and the variables from $W_i$ occupy exactly $l_i$ slots of $F.$ The factor $K(\bar{l})$ of $\hat{N}(\bar{w}, \bar{l})$ counts how the $l_i$ slots available for $W_i$ are distributed over the left-hand-sides of the equations. The second factor counts how to place the variables into their slots. Note that the right-hand-side of an equation cannot be chosen, it is determined by the value of the left-hand-side under $a, b.$

We abbreviate ${n \choose \bar{w}}\,= \, { n \choose w_0, w_1, w_2}. $ Given an assignment $a, $ $\bar{w}, $ and $\bar{l}, $ the number of assignment formula pairs $(b, F)$ with : There exist $\overline{W}$ with $\sharp W_i= w_i,$ such that $b \in D(a, \overline{W}),$ $F$ is true under $a$ and $b$, and the variables from $W_i$ occupy exactly $l_i$ slots of $F$ is $$\begin{aligned}
N( \bar{w}, \, \bar{l})\,
:= {n \choose \bar{w}} \cdot \hat{N}( \bar{w}, \, \bar{l}). \, \, \mbox{ This implies  } \, \,  \mbox{E}[X^2]\,= \, 3^n \cdot  \sum_{\bar{w},  \bar{l}}\, N(\bar{w}, \,\bar{l}) \cdot  \frac{1}{3^m \cdot N_0}.  \label{EWQU} \end{aligned}$$

Theorem \[EX2\] follows directly from the next theorem:

\[EX2EI\] $\sum_{\bar{w}, \bar{l}}  N(\bar{w}, \bar{l})/N_0 \, \le \, C\cdot 3^{(1- \gamma )n} .$

One more piece of notation: 