diff --git a/markdown/course7_advanced.md b/markdown/course7_advanced.md
index ebc6c75..d87a5c2 100644
--- a/markdown/course7_advanced.md
+++ b/markdown/course7_advanced.md
@@ -69,7 +69,7 @@ Example:
 
 ### Part-of-Speech Tagging (POS)
 
-We wish to predict an output vector $\textbf{y} = (y_{1}, y_{1}, ..., y_{L})$, of random variables, given an observed characteristic vector $\textbf{x} = (x_{1}, x_{2}, ..., x_{L})$
+We wish to predict an output vector $\textbf{y} = (y_{1}, y_{2}, ..., y_{L})$, of random variables, given an observed characteristic vector $\textbf{x} = (x_{1}, x_{2}, ..., x_{L})$
 
 $\textbf{y}$ takes it value from a list of $N$ possible values.
 
@@ -258,7 +258,7 @@ $$\mathcal{L}_{CE} = - \frac{1}{N} \sum_{n'=1}^{N}y^{(n)}.log(f(\textbf{x}, \the
 
 $$\mathcal{L}_{BCE} = - y^{(n)}.log(f(\textbf{x}, \theta)^{(n)}) + (1 - y^{(n)}).(1 - f(\textbf{x}, \theta)^{(n)})$$
 
-$$\mathcal{L}_{KL} = - \frac{1}{N} \sum_{n'=1}^{N}y^{(n)}.log(\frac{y^{(n)}}{f(\textbf{x}, \theta)^{(n)}})$$
+$$\mathcal{L}_{KL} = \frac{1}{N} \sum_{n'=1}^{N}y^{(n)}.log(\frac{y^{(n)}}{f(\textbf{x}, \theta)^{(n)}})$$
 
 ---