Jeremy Kun, a mathematics PhD student at the University of Illinois in Chicago, has posted a wonderful primer on probability theory for programmers on his blog. It's a subject vital to machine learning and data-mining, and it's at the heart of much of the stuff going on with Big Data. His primer is lucid and easy to follow, even for math ignoramuses like me.
For instance, suppose our probability space is and is defined by setting for all (here the “experiment” is rolling a single die). Then we are likely interested in more exquisite kinds of outcomes; instead of asking the probability that the outcome is 4, we might ask what is the probability that the outcome is even? This event would be the subset , and if any of these are the outcome of the experiment, the event is said to occur. In this case we would expect the probability of the die roll being even to be 1/2 (but we have not yet formalized why this is the case).
As a quick exercise, the reader should formulate a two-dice experiment in terms of sets. What would the probability space consist of as a set? What would the probability mass function look like? What are some interesting events one might consider (if playing a game of craps)?
Probability Theory — A Primer
(Image: Dice, a Creative Commons Attribution (2.0) image from artbystevejohnson's photostream)
Forget “disrupting” some industry — work at EFF and you can write code to make a better future for everyone!
Last week, 30 students used a House Judiciary Committee hearing room to hold a debate on mass surveillance in America.
The $80 Ramones 40th Anniversary Deluxe Edition collects 3 CDs, one LP and a hardcover book, in a limited, numbered box (the edition is limited to 19,760, which is a number you can interpret as either symbolic of the year 1976, or “this edition limited to the number we anticipate selling”).
Jared Sinclair developed the RSS reader app Unread, which made $10,000 in its first 24 hours on the iOS market. And we’ve all heard the story of Flappy Bird developer Dong Nguyen, whose creation was reportedly earning $50,000 a day at the height of its 2013 explosion. While those are rare examples, they’re also testament to the […]
If you or your company’s IT system are besieged by black hat cyber attacks, an ethical hacker might be all that stands between crippling damage and a company’s long-term prosperity. It’s no wonder that the market for IT security specialists is exploding. Certification is the key – so learn the tenets of ethical hacking and get […]
Your laptop and mobile devices are top of the line…so why are you trotting out that raggedy decades-old suitcase when you go somewhere? Time to up your travel game with a complete 5-piece Herschel Travel Luggage bundle…and we’ll even give it to you for free!Of course, you’ve got to win the Ultimate Herschel Travel Bundle […]