$page_title       = "Exhibit: Betting probability";
$page_description = "Exhibit page in Math 21b, Linear Algebra and Applications";
${base}           = "../../";
$robots = "all";

sub main_page {
print OUTPUT<<"EOF"

<h1> Betting probability </h1> 

One of the central applications of linear algebra is in statistics. 
Data fitting problems can be reformulated as projection problems. 
One of the reason to fit data is to understand the data better or
even to make predictions. If there is a trend, then very likely this
trend is going to continue. But this is not necessarily the case and 
often, it is difficult to actually predict the future. This was illustrated
in the Superbowl game of last weekend, where the odds of winning for
the Patriots was very low. Then came the turn. An image of the 
Washington Post illustrates this. It displays the probability which
was assessed for a Patriot win of the game at each moment of the game. 
You see that the probabiliy was almost zero between half time and the
end of the 3rd quarter. There had been a particularly interesting 
moment at the end of the game, where a coin toss decided who would start.
At that moment, the probability was assessed to be 50 percent.
 

<center>
<img src="betting.jpg"><br>
<a href="https://img.washingtonpost.com/news/fancy-stats/wp-content/uploads/sites/28/2017/02/NEATL.jpg">Source</a><br>
(Thanks to Paul Hermany to send this link.)
</center>

EOF
}

1;