ergodicity

report/report.tex

@@ -245,6 +245,10 @@ Nassim Taleb in \textit{Fooled By Randomness} describes this event with an analo
 1/10,000 chance of harm?  In this case, many less-than-rational actors use the game repeatedly to acquire wealth indefinitely, forgetting or even outright ignorant 
 that eventually the unlikely, or, as the actor would see it, the unthinkable, happens and all of the gains are completely negated.
 
+Averaging a game of Russian Roulette leaves the average person \$833,333 richer, but this is where ergodicity comes into play.  There is no 'average' person, 
+you can play and win many times but when you eventually bust you lose everything you put in.  Removing the vocabulary from this concept, averaging many first 
+iterations will not necessarily predict the performance of an experiment with many iterations.
+
 \subsubsection{Fooled By Randomness}
 While most statisticians are familiar with techniques to remove noise to get a clearer picture of long-term trends, many forget that noise over longer terms can 
 materialize as highly improbable events.  For instance, it is improbable to flip a fair coin and have heads land face up 5 times in a row, but if the coin is flipped 
@@ -734,7 +738,7 @@ calculated:
     Two consecutive sunny days:
     \[(\frac{5}{6} * .95) * (.9 * .95) \approx 0.677 \]
     Cloudy, Sunny:
-    \[(\frac{1}{6} * .6) * (.1 * .95) = 0.0095 \]
+    \[(\frac{1}{6} * .6) * (.5 * .95) = 0.048 \]
 \end{center}
 
 Hence, we can eliminate the \([\text{Cloudy, Sunny}]\) starting sequence from the most probable sequence of steps given the observations.  Doing the same thing