# Department of Statistics, The Ohio State University Statistics and Biostatistics Colloquium Series

## A Discrete Probability Problem on Dermal Patches

### M. B. Rao Department of Statistics, University of Cincinnati

#### 3:30PM - Thursday, May 1, 2008 Room 170, Eighteenth Avenue Bldg. (EA 170)

##### ABSTRACT

A dermal patch is designed to deliver doses of a certain medicine incrementally over a period of ten days. On the first day, the patch delivers one dose of medicine, second day two doses, third day three doses, and so on. The objective of the medicine is to make ten receptors inside the organism active. To start with, all receptors are inactive. The single dose delivered on the first day latches onto one of the receptors and makes it active. Two doses delivered on the second day latch onto two receptors, one dose per receptor. If the receptor is already active, the new dose makes it inactive. If the receptor is inactive the new dose makes it active. Three doses delivered on the third day latch onto three receptors, one dose per receptor. If the receptor is already active, the new dose makes it inactive. If the receptor is inactive the new dose makes it active. An so on. At the end of the tenth day how many receptors are expected to be active? A solution to this problem will be presented. Some generalizations will be formulated and discussed.

Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.