Ask a probabilist
In an effort to find something interesting to do with what I assume will be my last 21 posts as an "adept" (whatever that is), I decided to start this thread. Some may know already, but for those that do not, I am a probabilist (a mathematician who specializes in probability theory). If you have any burning questions you would like to ask a probabilist, then here is your chance. Post them here and I will try to answer them.
I can obviously answer questions regarding undergraduate mathematics, and basic graduate-level, measure-theoretic probability, including topics such as Markov chains, Brownian motion, and stochastic differential equations.
When it comes to more advanced topics, I can probably only answer questions within my field. I usually work on limit theorems for stochastic processes. This typically involves finding analogues of the law of large numbers and the central limit theorem, which apply to continuous-time processes. A simple example of this type of theorem is Donsker's theorem.
I am not a statistician, I do not work in numerical analysis or computing, and I do not work on discrete probability. I am no expert on philosophical issues related to probability, but I have read and thought about this topic a little bit and can offer my opinions. I can also offer some advice to graduate students about selecting an adviser, looking for a job, and so on.
But feel free to ask anything and I will do my best.
3 Replies
1. What are the odds of something with a fairly well established rate of occurrence of 65% happening 31 times in a row at any point within a sample of 4000 trials?
2. Are there any implications of the Mandelbrot Set for philosophy, metaphysics, quantum mechanics, probability theory, etc. ... that can be stated in "lay person" non-mathematical terms?
Yes.
A lot of people with a background in probability go into the financial industry. Also, with a little work, a probabilist can usually pass for a statistician, which obviously opens up a lot of jobs everywhere.
Years ago, when I worked for Northrop (now Northrop-Grumman) my job was with reliability engineering which is actually a blend of probability theory and engineering (and I knew little about engineering). They called me a mathematician, but I really was working as a probability expert and also did mathematical modeling. So, that's another occupation where this knowledge can be used.
1. What are the odds of something with a fairly well established rate of occurrence of 65% happening 31 times in a row at any point within a sample of 4000 trials?
This is not really the sort of thing a probabilist does. It would be like asking a research engineer at Ford to change the oil on your car. But that said, here is a website that can calculate it: https://www.profitduel.com/betting-calcu.... According to that calculator, the answer is about 1 in 454.
2. Are there any implications of the Mandelbrot Set for philosophy, metaphysics, quantum mechanics, probability theory, etc. ... that can be stated in "lay person" non-mathematical terms?
There are no specific implications of the Mandelbrot set for probability theory that I know of. The Mandelbrot set is an example of a fractal, and people do study stochastic processes that live on fractals, so they are not mathematically unrelated. But the connection between the two feels rather generic to me.
