From 8dd0a75e35cf23c8be1f61057c5b66c2bd235492 Mon Sep 17 00:00:00 2001
From: Thibaut Horel <thibaut.horel@gmail.com>
Date: Tue, 7 Oct 2014 09:16:31 -0400
Subject: Typo fixes

---
 ps2/main.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'ps2/main.tex')

diff --git a/ps2/main.tex b/ps2/main.tex
index c4a4ad3..360d88a 100644
--- a/ps2/main.tex
+++ b/ps2/main.tex
@@ -34,7 +34,7 @@
 \newtheorem{lemma}{Lemma}
 
 \author{Thibaut Horel}
-\title{CS 229r Problem Set 2 -- Solutions}
+\title{CS 224 Problem Set 2 -- Solutions}
 
 \begin{document}
 
@@ -235,7 +235,7 @@ determined once $h(x)$, $h(y)$ and $h(z)$ have been observed.
         \item By construction all the elements in $T'$ have
             different characters at position 0 and different from the
             characters at position 0 of the words in $T'$. Hence, the given words
-            in $T$, $\mathca{H}$ behaves completely randomly on $T'$ by the
+            in $T$, $\mathcal{H}$ behaves completely randomly on $T'$ by the
             same observation as the one we used in \textbf{(b)}. But by the
             induction hypothesis, $\mathcal{H}$ behaves completely randomly on
             $T$. As a consequence $\mathcal{H}$ behaves completely randomly on
@@ -257,7 +257,7 @@ where the second inequality follows from the lemma. Now applying a union bound:
     \Pr[l\geq k] &\leq \sum_{S,\, |S| = \log k}\Pr[S\text{ maps to $L$ and
     $\mathcal{H}$ random over $S$}]\\
     &\leq\binom{n}{\log k}m\frac{1}{m^{\log k}}
-    \leq\frac{n^\log k}{(\log k)!}\frac{1}{m^{\log k -1}}
+    \leq\frac{n^{\log k}}{(\log k)!}\frac{1}{m^{\log k -1}}
 \end{align*}
 Using $m> n^{1.01}$, we get:
 \begin{displaymath}
-- 
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