diff --git a/doc/Hybrid.lyx b/doc/Hybrid.lyx
index 3067d5c26..44df81e39 100644
--- a/doc/Hybrid.lyx
+++ b/doc/Hybrid.lyx
@@ -264,11 +264,34 @@ If we take the log of
  we get
 \begin_inset Formula 
 \begin{equation}
-\log P(x|y,m)=\log P_{m}(x|y)=K_{gcm}-E_{gcm}(x,y).\label{eq:gm_log}
+\log P(x|y,m)=\log P_{m}(x|y)=K_{gc}(m)-E_{gcm}(x,y).\label{eq:gm_log}
 \end{equation}
 
 \end_inset
 
+
+\end_layout
+
+\begin_layout Standard
+\noindent
+For conciseness, we will write 
+\begin_inset Formula $K_{gc}(m)$
+\end_inset
+
+ as 
+\begin_inset Formula $K_{gcm}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\SpecialChar allowbreak
+
+\end_layout
+
+\begin_layout Standard
+\noindent
 The key point here is that 
 \family roman
 \series medium
@@ -307,7 +330,7 @@ GaussianMixture
 \begin_inset Formula $m$
 \end_inset
 
-, and is not dependent on the value of 
+, and cannot be dependent on the value of 
 \begin_inset Formula $m$
 \end_inset
 
diff --git a/doc/Hybrid.pdf b/doc/Hybrid.pdf
index 456ce49c4..182573412 100644
Binary files a/doc/Hybrid.pdf and b/doc/Hybrid.pdf differ