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)
Ladder lockdown is a metal tray with super-grippy patches on its underside; set it down on any surface (including ice!) and then set your ladder’s feet in the tray and cinch it in place and the ladder won’t “kick out” and injure you and your loved ones.
Machinist/sculptor Chris Bathgate (previously) continues his run of collaborations on small, gorgeous kinetic sculptures and fidget toys with the “Netsuke Hybrid Vessel Bead,” a collaboration with Revolve Makers.
There are three more stops on my tour for Walkaway: tomorrow at San Diego Comic-Con, next weekend at Defcon 25 in Las Vegas, and August 10th at the Burbank Public Library.
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