ChapterZero

I’ve been quiet for a while because I’ve been studying probability, with an eye towards learning Markov fields and the Gibbs sampler, so I’ll be able to contribute to the new tissue model. This is not as easy as I thought– definitely not just another branch of measure theory– so I’ve been consulting several different books. Here’s a problem from one that I posted to the math group’s mailing list:

Mrs. Jones has made a steak and kidney pie for her sons. Eating more
than half of it will give indigestion to anyone. While she is away
having tea with a neighbor, the older son helps himself to a piece of
the pie. Then, the younger one comes and has a piece of what is left.
When Mrs. Jones returns, she finds that more than half of the pie is
gone.

Assuming that the size of each of the two pieces eaten is random and
uniformly distributed over what is currently available, what is the
probability that neither of Mrs. Jones’ sons will get indigestion?

If we let be the amount of pie the older brother eats, and the amount the younger brother eats, the hard part of this problem is seeing that the density is not constant.