improved text for mutual information project

projects/project_mutualinfo/mutualinfo.tex

@@ -19,26 +19,34 @@
   object was reported by the subject. 
   
   \begin{parts}
-    \part Plot the data appropriately. 
+    \part Plot the data appropriately.
+
     \part Compute a 2-d histogram that shows how often different
-    combinations of reported and presented came up. 
+    combinations of reported and presented came up.
+
     \part Normalize the histogram such that it sums to one (i.e. make
     it a probability distribution $P(x,y)$ where $x$ is the presented
     object and $y$ is the reported object). Compute the probability
     distributions $P(x)$ and $P(y)$ in the same way.
+
     \part Use that probability distribution to compute the mutual
-    information $$I[x:y] = \sum_{x\in\{1,2\}}\sum_{y\in\{1,2\}} P(x,y)
-    \log_2\frac{P(x,y)}{P(x)P(y)}$$ that the answers provide about the
-    actually presented object. 
+    information 
+    \[ I[x:y] = \sum_{x\in\{1,2\}}\sum_{y\in\{1,2\}} P(x,y)
+    \log_2\frac{P(x,y)}{P(x)P(y)}\] 
+    that the answers provide about the actually presented object.
 
     The mutual information is a measure from information theory that is
     used in neuroscience to quantify, for example, how much information
     a spike train carries about a sensory stimulus.
+
     \part What is the maximally achievable mutual information (try to
     find out by generating your own dataset which naturally should
     yield maximal information)?
-    \part Use bootstrapping to compute the $95\%$ confidence interval
-    for the mutual information estimate in that dataset. 
+
+    \part Use bootstrapping (permutation test) to compute the $95\%$
+    confidence interval for the mutual information estimate in the
+    dataset from {\tt decisions.mat}.
+
   \end{parts}
 
 \end{questions}