Stochastic Processes are fun!
I never thought I would enjoy statistics, but since I’m taking a course on stochastic processes this semester, and I know just about nothing about statistics, I started doing some reading. I checked out the classic– and deservedly so– ‘Probabiliy, Random Variables, and Stochastic Processes’ by Papoulis, et. al. I haven’t had time to read anything more than the first five chapters, but that’s enough to let me know how interesting this material is. And looking at the title of the following chapters is making me salivate. Too bad that someone put in a request for it, so I have to return it to the library by the 18th.
I suspect part of the reason I disliked statistics in the past is the way that the reasoning and non-trivial calculations that motivate certain definitions get cut out completely, and the class is reduced to plug and chug. Like, where did the 
statistic come from? I don’t know, but I can– or rather, I could when I was taking the engineering stats class– tell you how to use it in this formula to calculate this… A lot of the beauty I’m seeing now arises from the struggle to manage the complexity of the calculations involved, which leads to some clever definitions and ideas. To be as vague as possible 
At the same time I’m taking the stochastic processes course from an engineering perspective, I’m also taking a math course in measure theory, which despite the fact that it is not aimed at a measure theoretic interpretation of probability theory, is giving me some neat ideas and insights on the stuff we’re just to memorize for the engineering course. E.g., why the cdf of a random variable is always right continuous.
We haven’t covered anything spectacular in class yet; so far, the most interesting things we’ve done are integral calculations of the sort you probably only see in probability theory, and using the characteristic function and moment generating function. Hopefully by the end of the semester, I’ll have a good idea of what Markov chains are, and how to use them in applications. And, some statistical signal processing tools in my kit
Possibly relevant posts:
- ACM 116: Stochastic Processes (10/11/2006)
- Orlicz spaces (10/5/2008)
- Demographics in Technical Fields (8/24/2005)