bugfix

content/CSE5313/CSE5313_L15.md

@@ -140,6 +140,7 @@ $$
 \begin{aligned} 
 H(Y|X=x)&=-\sum_{y\in \mathcal{Y}} \log_2 \frac{1}{Pr(Y=y|X=x)} \\
 &=-\sum_{y\in \mathcal{Y}} Pr(Y=y|X=x) \log_2 Pr(Y=y|X=x) \\
+\end{aligned}
 $$
 
 The conditional entropy $H(Y|X)$ is defined as:
@@ -150,6 +151,7 @@ H(Y|X)&=\mathbb{E}_{x\sim X}[H(Y|X=x)] \\
 &=-\sum_{x\in \mathcal{X}} Pr(X=x)H(Y|X=x) \\
 &=-\sum_{x\in \mathcal{X}, y\in \mathcal{Y}} Pr(X=x, Y=y) \log_2 Pr(Y=y|X=x) \\
 &=-\sum_{x\in \mathcal{X}, y\in \mathcal{Y}} Pr(x)\sum_{y\in \mathcal{Y}} Pr(Y=y|X=x) \log_2 Pr(Y=y|X=x) \\
+\end{aligned}
 $$
 
 Notes: