A review of probability theory (opens in new tab)

Well, the hacker news feature a lot of programming-related stuff that is certainly 'above' the (average) blog post level (in the whole blogosphere). I know of no better meta-filter than hacker news for blog entries attracting a hacker's mindset. Certainly, the appreciation for mathematical thinking as well as mathematical methods plays a big role in this (analytic) mind set.

While the novice programmer might not get (the content and purpose of) python vs. ruby comparisons and the like, readers with a weak background in math will not find this probability entry useful (or too 'difficult').

However, for a certain subset of all hacker news readers, which are looking to dig deeper, it is a very nice resource.

Hacker news, to me, is especially useful since it provides links which are well distributed in terms of this 'entry level'.

Yes. I think this exceeds the capacity of the blog medium.

> What percentage of students after having passed a probability course can define a random variable?

In a typical probability theory course, all of them, hopefully. I found random variables to be a crucial part of my probability theory class, being used in almost all (if not all) topics after the first month.

There are certainly other approaches to learning probability theory (though perhaps not what you were thinking.) I understand that E.T. Jaynes' book on probability theory, which I have not yet read, does not go the route of random variables.

A better question would be: what percentage understand what a random variable is and will be able to apply this understanding later. See http://www.youtube.com/watch?v=WwslBPj8GgI for exploration of the difference by a Harvard physics professor who realized a few years into his teaching career that most of his into physics students weren't learning very much, although they were able to apply all the appropriate mathematical recipes to all the standard type homework and exam questions.

I think your point is true when it comes to teaching introductory probability or perhaps even a second and third course in probability. However, at some point, it becomes necessary to dive into things formally.

This blog entry is meant for a review for a graduate level course, so it makes sense that it runs through a lot of formal definitions.