Kinetically Constrained A place to keep the longer thoughts of Doug Ashton.
Posts with the tag probability:

Tree diagrams solve everything

Just a quick one. I saw this post, When intuition and math probably look wrong, via Ben Goldacre’s mini blog. The problem is set as follows: I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys? Intuition tells you the answer is 1/2, mathematicians tell you it’s something else. I’ll leave the answer until the end of the post in case you want to run off and solve it first. It’s essentially a fancier version of the Monty Hall problem. The Science News article deals with this just fine so I don’t really want to expand on it.

Bootstrapping: errors for dummies

The trouble with science is that you need to do things properly. I’m working on a paper at the moment where we measured some phase diagrams. We’ve known what the results are for ages now, but because we have to do it properly we have to quantify how certain we are. Yes, that’s right. ERRORS! I’ve come on a long way with statistics, I’ve learned to love them, I defy anyone to truly love errors. However, I took a step closer this month after discovering bootstrapping. It’s a name that has long confused me, I seem to see it everywhere. It comes from the phrase “to pull yourself up by your boot straps”.

An unintuitive probability problem

Probability can do strange things to your mind. This week I had a probability problem where every time I tried to use intuition to solve it I ended up going completely wrong. I thought I’d share it as I think it’s interesting. Consider a one dimensional random walk. At each time step my walker will go left with probability \(p_l\), and right with probability \(p_r\). It stays where it is with probability \(1 - p_l - p_r\). Furthermore these probabilities are dependent on the walker’s position in space, so it’s really \(p_l(x)\) and \(p_r(x)\). I’m imagining I’m on a finite line of length, L, although it doesn’t matter too much.