NYU Probability Summer 2009

conditional probability, baye's probabilities, independent events

I pulled this up from the MIT Open CourseWare page under their Problem Solving class. I think they use problems of this caliber to prepare for the Putnam exam.

OK, I now know two ways to solve this. The first way was along the lines you described in the break to me, Sam. It makes more sense than I originally thought, and with your Discrete Math knowhow you might be able to solve it. There's also a clever way, which I admit I didn't figure out until I solved it the other way.

That's a great list of problems btw!

Normal distributions for people with a flair for linear algebra :).

Mandlebrot argues that markets do not follow a normal distribution. An interesting book from the man behind the Mandlebrot set.

thanks for this. Dr. Mandlebrot seems to be always ahead of his time.

A 1-minute long lecture from the tv show Numb3rs about the famous Monty Hall problem.

I blogged about Numb3rs a few years back: http://www.math.harvard.edu/~leingang/index.php/is-numb3rs-for-real.html

Not so much relevant to probability but a nice story and it mentions an NYU professor.

This is for those who wondered what a degree in math can get!

The rising stature of statisticians, who can earn $125,000 at top companies in their first year after getting a doctorate, is a byproduct of the recent explosion of digital data. In field after field, computing and the Web are creating new realms of data to explore - sensor signals, surveillance tapes, social network chatter, public records and more. And the digital data surge only promises to accelerate, rising fivefold by 2012, according to a projection by IDC, a research firm.

When baseball dubbed shortstop Harold Reese "Pee Wee" and first basemen Fred Merkle "Bonehead," they probably weren't trying to lengthen the players' lives. But according to researchers at Wayne State University, major-league players who have nicknames live 2½ years longer, on average, than those without them. The nickname findings are part of the wide-ranging and often arcane academic research that deals with the national pastime. In another study, we learn that players whose first or last name begins with "K" strike out more than those without "K" initials. And in case you were wondering, research finds Democrats support the designated-hitter rule more than Republicans.

the initial K effect really gets me, probably because the human tendency to try and explain it does not work. The original paper is here and contains an additional study which found that "students whose names began with 'C' or 'D' earned lower GPAs than students whose names began with 'A' or 'B.'" http://papers.ssrn.com/sol3/papers.cfm?abstract_id=946249 Here is some criticism of the study. http://sabermetricresearch.blogspot.com/2007/11/k-study-for-real_26.html http://skepstat.blogspot.com/2007/12/why-i-am-javascript-master.html

I have no Erdos number as I have not published any joint papers. Also, I'm offended with the slander against Kevin Bacon as a "not too well known American actor." Have you ever heard of Footloose?

I like the math joke at the beginning.

This is really cool. A brief exposure to how computers are able to play chess.

the data, pure and simple

What's the length of a random chord in a circle? It turns out that even if you try to distribute the chord uniformly there is an ambiguity.

I spiffed up and posted the GeoGebra worksheet if you're interested.

Bertrand's Paradox is a question in continuous probability that shows the perils of uniformly distributed variables. The question is simple: given a random chord in a circle, what's the probability that it's longer than the side length of an equilateral triangle inscribed in that circle?