From 9aaecdf4ce93727a435251015d0e592f8c0e0021 Mon Sep 17 00:00:00 2001
From: caprice-j <tnk.yasutaka@gmail.com>
Date: Sun, 13 Aug 2017 00:44:06 -0500
Subject: [PATCH] fixed a typo in a binomial identity

---
 latex/intro.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/latex/intro.tex b/latex/intro.tex
index ba8630d6..238af3bb 100644
--- a/latex/intro.tex
+++ b/latex/intro.tex
@@ -735,7 +735,7 @@ \subsection{Randomization and Probability}
 \end{align*}
 This requires that we know enough to calculate that $\Pr\{X=i\}
 = \binom{k}{i}/2^k$, and that we know the binomial identities
-$i\binom{k}{i}=k\binom{k-1}{i}$ and $\sum_{i=0}^{k} \binom{k}{i} = 2^{k}$.
+$i\binom{k}{i}=k\binom{k-1}{i-1}$ and $\sum_{i=0}^{k} \binom{k}{i} = 2^{k}$.
 
 Using indicator variables and linearity of expectation makes things
 much easier.  For each $i\in\{1,\ldots,k\}$, define the indicator