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)
Zachary Zmith writes, “A Kickstarter is funding beautifully-designed and illustrated editions of classic stories, with illustrations from Paul Pope, Yuko Shimizu and Bill Sienkiewicz. They have already met their initial goal to fund a version of Algernon Blackwood’s ‘The Willows’ with art by Paul Pope. If they reach $100k, Bill Sienkiewicz will illustrate H.G. Wells’ […]
Asaf Hanuka is a celebrated Israeli cartoonist whose astonishing, surreal illustrations serve as counterpoint to sweet (sometimes too-sweet) depictions of his family life, his complicated existence as a member of a visible minority in Israel, the fear he and his family live with, and his own pleasures and secret shames — a heady, confessional, autobiographical brew that has just been collected into The Realist: Plug and Play, the second volume of Hanuka’s comics.
SOG’s $60 Sync II “wearable belt buckle” multitool isn’t the only multitool/buckle on the market, but it does add a couple very sensible innovations, like a clip-on/clip-off base that lets you use your tool without taking off your belt, and a squared-off form factor (like a pair of folding travel sewing scissors) that adapts the […]
If you don’t want to get stuck footing the bill for a hit and run, this dashboard-mounted camera offers up to 2K resolution to make sure you always have a reliable witness, and it’s available in the Boing Boing Store for 30% off it’s usual price.The PapaGo mounts unobtrusively to your windshield to see everything […]
While some people still maintain that everything in Apple’s walled garden “just works” and is immune to the rampant malware of the Windows world, the reality is different. The Mac’s growing market share has made it a much more viable target for malicious actors, and its built-in tools aren’t always enough to fix things. Drive […]
Boasting an IPX6 waterproof rating, the Trakk Bullet Ultra Compact Waterproof Bluetooth Speaker resists dust and heavy rainfall. It’s currently available in the Boing Boing Store.The Trakk Bullet offers the same wireless convenience as other portable speakers, but few are built as tough as this one. Its utilitarian construction is designed to be a totally low-maintenance […]