slides: more corrections

slides/sections/2.md

@@ -55,7 +55,7 @@
 ## Landau median
 
 - CDF computed by numerical integration
-- Mean computed by numerical root-finding
+- Median computed by numerical root-finding
 $$
   F(x) = \frac{1}{2} \thus m_L\ex = 1.3557804...
 $$

slides/sections/4.md

@@ -141,7 +141,7 @@ $$
     % placeholder
     \draw [transparent] (-2.7,-0.2) rectangle (3,3.3);
     % bandwidth 1
-    \node <4,5> [left] at (2.9,3) {$\epsilon = 1$};
+    \node <4,5> [left] at (2.9,3) {$\varepsilon = 1$};
     % points
     \draw <3-> [yellow!50!black, fill=yellow] (-1.2,-0.2) rectangle (-1,0);
     \draw <3-> [yellow!50!black, fill=yellow] (-0.1,-0.2) rectangle (0.1,0);

slides/sections/6.md

@@ -88,7 +88,7 @@
     \thus G\left( 0, \sqrt{e^{\mu_k}} \right)
   $$
 
-- The greater $\mu^k$, the 'larger' $G\left( 0, \sqrt{e^{\mu_k}} \right)$
+- The greater $\mu_k$, the 'larger' $G\left( 0, \sqrt{e^{\mu_k}} \right)$
 $$
 \begin{cases}
   \mu_k \longrightarrow + \infty \\
@@ -155,20 +155,20 @@ $$
 
 ::: incremental
 
-- Define the function $\vartheta (u)$ as:
-$$
-  \vartheta (u) = \frac{2}{\sqrt{r}}
-                  \left[ \sum_{j} \zeta_j (u) - \frac{r}{2} \right]
-$$
-
 - If $a_j$ uniformly distributed, by the CLT:
 $$
   \sum_j \zeta_j (u) \hence
     G \left( \frac{r}{2}, \frac{\sqrt{r}}{2} \right)
-  \thus \vartheta (u) \hence
-    G \left( 0, 1 \right)
 $$
 
+- Define the function $\vartheta (u)$ as:
+$$
+  \vartheta (u) = \frac{2}{\sqrt{r}}
+                  \left[ \sum_{j} \zeta_j (u) - \frac{r}{2} \right]
+  \to  G \left( 0, 1 \right)
+$$
+
+
 - Test statistic:
 $$
   \Theta = \int_{\underbar{u}}^{\bar{u}} du \, \vartheta^2 (u) \psi(u)