From e1bfd1dea934097e89ed1b0c9ae9c9ad653d7ecc Mon Sep 17 00:00:00 2001 From: Paul 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(-) 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} -- cgit v1.2.3-70-g09d2