What is the probability that in a box of a dozen donuts picked from 14 flavors there’s no more than 3 flavors in the box?

Problem

Dave’s Donuts offers 14 flavors of donuts (consider the supply of each flavor as being unlimited). The “grab bag” box consists of flavors randomly selected to be in the box, each flavor equally likely for each one of the dozen donuts. What is the probability that at most three flavors are in the grab bag box of a dozen?

Naïve Numerical Sums in R

Introduction

The Kolmogorov distribution (which I call $F(x)$) is as follows:

$F(x) = \frac{\sqrt{2 \pi}}{x} \sum_{k = 1}^{\infty} e^{-(2k - 1)^2 \pi^2/(8x^2)}$

High Dimensional Data, MSRI, and San Francisco in 2018; Reflections

Last fall my adviser alerted me to the MSRI workshop on high-dimensional data and suggested I may be interested. I applied and was accepted to participate. Thus, from July 9th to July 20th I stayed in San Francisco (for the first time in my life), living in the dorms of UC Berkeley and attending the workshop. I got to experience San Francisco’s legendary weather (escaping Salt Lake City’s triple-digit heat) while learning mathematics. I enjoyed the experience and wanted to share it.

Where to Go from Here? Tips for Building Up R Experience

At the University of Utah, I teach the R lab that accompanies MATH 3070, “Applied Statistics I.”” None of my students are presumed to have any programming experience, and they never hesitate to remind me of that fact, especially when they are starting out. When I create assignments and pick problems, I often can write a one- or three-line solution in thirty seconds that students will sometimes spend four hours trying to solve. They then see my solution and slap their foreheads at its simplicity. I can be tricky with my solutions. For example, suppose you wish to find the sample proportion for a certain property. A common approach (or at least the one used in the textbook our course uses, Using R for Introductory Statistics by John Verzani) looks like this: