NYU Probability Summer 2009

There are at least 3 conditional probabilities problems embedded in the article (it doesn't look like there are specific enough numbers to solve them precisely though).

whats is the truth for the Question 2?

Genetics for Probability

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?

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.

the data, pure and simple

related to the problem:a gambler with finite wealth, playing a fair game (that is, each bet has expected value zero to both sides) will eventually go broke against an opponent with infinite wealth

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!

A biography about magician-turned-mathematician (probabilist) Persi Diaconis as well as a look at his experiments to understand the bias of a coin flip.

Great article. Everything I've been saying about Diaconis I learned through oral tradition. It's good to know I was pretty much right on.

Funny, after reading the article I concluded that you must've either read this article or a similar biographical sketch. Diaconis must be some legend! One of my favorite parts was that he was a bit 'rough' at one point. Gives the rest of us some hope!

How Bayes's Theorem can be used to decide if mail is spam or not.

Very cool. Now that we see that mail filter software "adapts" to the user, we can address the problem in class of what would happen if a doctor who deals with prostate issues uses a filter and words such as viagra prop up when the email is not actually spam.

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

young einstein vs. old einstein why he changed his mind!

Some clips of events that are "probably" never gonna happen. Tells the probability of each event occurring.

Something tells me this is more of a photoshop and film editing problem than a probability problem. :)

very funny! and great marketing!

In case you wanted to know a more precise way to deal with all of the factorials we've been playing around with.

If you like Erdos, you should take Algebra with Joel Spencer. He collaborated with Erdos for 40 or more publications I think.

Far More Than You Ever Wanted To Know about where this formula comes from.

Stirling's approximation is for n! in terms of continuous functions.

The derivation didn't require any complex analysis after all; thank goodness.

using the poisson distribution to approximate the binomial distribution