Home > Mathematica, Mathematics > How many bumps?

How many bumps?

In lecture 10 of Professor Blitzstein’s STAT110 course he refers to a Putnam combinatorial problem.

The following extract is this problem:

Professor Blitzstein uses indicator variables to solve this. I found it instructive to think through his exposition and present it here:

To provide illustration I created both a CDF and the quicktime movie below. The number is not application of the formula but brute force counting of the maxima per permutation and then averaging. The inefficiency of this rises dramatically (as expected considering the number of comparisons per permutation). I left it at 6 for both computational convenience as well as ease of display.

Categories: Mathematica, Mathematics

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s

%d bloggers like this: