Remaining typos in P1

1 files changed, 2 insertions, 2 deletions

diff --git a/ps1/main.tex b/ps1/main.tex
index 0605359..84a6e7a 100644
--- a/ps1/main.tex
+++ b/ps1/main.tex
@@ -73,12 +73,12 @@ For agent 1,$$\Pr[v_1 \geq v_2] = \begin{cases} \int_{\frac{1}{2}}^{v_1} 2\,dx =
 For agent 1, $P_1^{SP}(v_1)$ equals $\E[v_2|v_1\geq v_2]\cdot \Pr[v_1 \geq v_2]$. By Revenue Equivalence (Corollary 2.5), for $i \in \{1,2\}$, $P_i^{SP}(v_i) = P_i^{FP}(v_i)$. 
 
 We directly compute $$\E[v_2|v_1\geq v_2] =  \begin{cases} \frac{1}{2}\big(v_1+\frac{1}{2}\big) &\text{ if } v_1 > \frac{1}{2} \\ 0 &\text{ if } v_1  \leq \frac{1}{2} \end{cases}$$
-Indeed, in expectation a uniform random variable evenly divides the interval it is over, and conditioned on $v_1\geq v_2$, $v_2$ is $U\big[\frac{1}{2},1\big]$. Thus, 
+Indeed, in expectation a uniform random variable evenly divides the interval it is over, and conditioned on $v_1\geq v_2$, $v_2$ is $U\big[\frac{1}{2},v_1\big]$. Thus, 
 $$s_1(v_1) =  \begin{cases} \frac{1}{2}\big(v_1+\frac{1}{2}\big) &\text{ if } v_1 > \frac{1}{2} \\ 0 &\text{ if } v_1  \leq \frac{1}{2} \end{cases}.$$
 
 For agent 2,  $$\Pr[v_2 \geq v_1] =  \int_{0}^{v_2}\,dx = v_2$$
 
-Computing $$\E[v_1|v_2\geq v_1] =  \int_0^{v_2} x\,dx = \frac{v_2}{2}$$
+Computing $$\E[v_1|v_2\geq v_1]  = \frac{v_2}{2}$$
 since conditioned on $v_2\geq v_1$, $v_1$ is $U\big[0,v_2\big]$.
 
 So $$s_2(v_2) = \frac{v_2}{2}.$$