From e1bfd1dea934097e89ed1b0c9ae9c9ad653d7ecc Mon Sep 17 00:00:00 2001
From: Paul <Paul@Pauls-MacBook-Air.local>
Date: Mon, 20 Oct 2014 11:50:15 -0400
Subject: [ps2] fixing 4.19 some more

---
 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 765c399..692654c 100644
--- a/ps2/main.tex
+++ b/ps2/main.tex
@@ -70,9 +70,9 @@ Next, we consider $REF_{\neq}$.
 \begin{align}
 REF_{\neq} &= \sum_{\substack{i \in I}}\E[\phi_i(v_i) | i \neq {\psi(i)}] \Pr[i\neq {\psi(i)}] \\
 &\leq \sum_{\substack{i \in I}}\E[v_i | i \neq {\psi(i)}] \Pr[i\neq {\psi(i)}] \\
-&\leq \sum_{\substack{i \in I}}\E[\hat{v}_i | i \neq {\psi(i)}] \Pr[i\neq {\psi(i)}]  \\
-&= \sum_{\substack{i \in I}}\E[v_{\psi(i)} | i \neq {\psi(i)}] \Pr[i\neq {\psi(i)}] \label{428} \\
-&\leq \sum_{\substack{i \in I}}\E[v_{\psi(i)} | i = {\psi(i)}] \Pr[i={\psi(i)}] +  \sum_{\substack{i \in I}}\E[v_{\psi(i)} | i \neq {\psi(i)}] \Pr[i\neq {\psi(i)}] \label{429} \\
+&\leq \sum_{\substack{i \in I}}\E[p_{\psi(i)}({\mathbf v}) | i \neq {\psi(i)}] \Pr[i\neq {\psi(i)}] \label{428} \\
+&\leq \sum_{\substack{i \in I}}\E[p_{\psi(i)}({\mathbf v}) | i = {\psi(i)}] \Pr[i={\psi(i)}] +  \sum_{\substack{i \in I}}\E[p_{\psi(i)}({\mathbf v}) | i \neq {\psi(i)}] \Pr[i\neq {\psi(i)}] \label{429} \\
+&= \sum_{i \in I} \E[p_{\psi(i)}({\mathbf v})] \\
 &= APX.
 \end{align}
 
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