# Posts

### A Dice Probability Problem

Here is an interesting problem having to do with dice and probability. Take a normal, fair die. Instead of labeling the faces with the …

### Polynomial Interpolation

It is interesting to look at what happens when you try to “fit” the absolute value function using polynomials. Pick some …

### Another Parabola Construction

Building on my last post, here is another way to construct a parabola using a collection of straight lines. First, the description, …

### Constructing Parabolas with Mathematica

There are several ways to draw a parabola using straight lines. If you get a chance, you should try one sometime - it is always …

### A Quasiperiodic Counterexample

The problem Consider a function $$f: [0, 1] \to \mathbb{R}$$ that is continuous with $$f(0) = f(1)$$. It is possible to prove that for …

### A Function Golf Challenge

“Code golf” is the practice of trying to solve a specific problem or implement a specific algorithm in the smallest possible number of …

### The Perfect Math Library Doesn't Exi-

Introduction Many mathematicians have a rough mental list of “desert island” books - a small set of books they would choose if stranded …

### Bootstrapping LOWESS

In chapter 1 of their 2016 book Computer Age Statistical Inference, Bradley Efron and Trevor Hastie use as an example a study of kidney …

### Bayesian Estimation of Multinomial Parameter Ratios

Consider a multinomial distribution with $$c$$ categories and associated probabilities $$\pi_i$$, where $$i = 1,...,c$$. It is often …

### Simpson’s Paradox: A Tale of Two Carpenters

Once upon a time, in a small town, there were two carpenters: Bob and Tom. Bob was an honest, hardworking carpenter with a good …