# A Drug-Induced Random Walk

@article{Velleman2014ADR, title={A Drug-Induced Random Walk}, author={Daniel J. Velleman}, journal={The American Mathematical Monthly}, year={2014}, volume={121}, pages={299 - 317} }

Abstract The label on a bottle of pills says “Take one half pill daily.” A natural way to proceed is as follows: Every day, remove a pill from the bottle at random. If it is a whole pill, break it in half, take one half, and return the other half to the bottle; if it is a half pill, take it. We analyze the history of such a pill bottle.

## References

SHOWING 1-10 OF 13 REFERENCES

Extensions of the birthday surprise

- Mathematics
- 1967

Abstract The so-called “birthday surprise” is the fact that, on the average, one need only stop about 24 people at random to discover two who have the same birthday. Here we determine,…

Random Walk: A Modern Introduction

- Computer Science
- 2010

This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice and is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

What to Expect in a Game of Memory

- Computer ScienceAm. Math. Mon.
- 2013

The game of memory is played with a deck of n pairs of cards and it is determined that, when the game is played optimally, the expected number of moves is (3 − 2 ln 2)n + 7/8 − 2Ln 2 ≈ 1.61n.

On Birthday, Collectors', Occupancy and Other Classical Urn Problems

- Mathematics
- 1986

Summary An urn contains r different balls. Balls are drawn with replacement until any k balls have been obtained at least m times each. How many draws are necessary? How many balls have been drawn…

An Introduction To Probability Theory And Its Applications

- Computer Science
- 1950

A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.

On the birthday problem: some generalizations and applications

- Mathematics
- 2003

We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of…

A Birthday.

- MedicineJAMA oncology
- 2016

A brief history of the development of an approach to helping students learn mathematical concepts at the post-secondary level using ISETL, a programming language derived from SETL, to implement instruction whose design is based on an emerging theory of learning.

Digital Library of Mathematical Functions

- Computer Science
- 2003

This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.

Matching balls drawn from an urn

- Problem E 2263, Solutions by B. C. Arnold and R. J. Dickson, Amer. Math. Monthly 78
- 1971