Problems from life

Every so often I come across interesting math problems from the news, twitter, etc. which you probably wouldn't find in a textbook. I'm sharing them here.

The distribution of unpecked chicks (link)

I learned about this problem from a tweet and then spent two entire flights figuring it out. I never thought I'd spend so much time thinking about chickens.

Elchanan Mossel's dice problem (link)

A truly wonderful yet unassuming dice problem to test your intuition about conditional probability.


Notes

Here are some notes from courses I've taken or self-teaching. Be warned that they are very rough and probably rife with errors.

The Heckman correction: an introduction (link)

I learned about the Heckman correction in college but I never really understood it until I had to use it for a project during Data Science for Social Good in 2016.

Brief Primer to Random Trees (link)

An introduction to the core concepts in the theory of random trees, taken from two lectures in STOR 831 (Weak convergence). Sets up notation and definitions for the main convergence theorems of simply-generated trees and so forth.

Inequalities: basic primer (link)

Overview of tools that anybody in any field tangentially related to statistics ought to know. A subset of the two sources above, but more polished and with some commentary.

STOR 654: Statistical Theory 1 (link)

Basic decision theoretic framework and the usual point estimation/hypothesis testing/confidence sets. Some newer material towards the end but I got lazy and didn't finish them.

STOR 634: Measure Theory (link)

Basic measure theory course. Included only sketches of the proofs in order to help me to internalize the proof concepts. Probably not complete towards the end, either.

STOR 635: Probability (link)

First course in graduate probability. Assumes knowledge of measure theory although there is a baby introduction of the basics at the beginning.