## Date of Submission

Spring 2018

## Academic Programs and Concentrations

Mathematics

## Project Advisor 1

Maria Belk

## Project Advisor 2

Amir Barghi

## Abstract/Artist's Statement

The goal of this project is to find the expected value and standard deviation of the center of mass in selected random configurations. The center of mass, which is a unique point in a system where the mean distribution of the mass is located, is calculated by dividing the sum of all of the the masses times the position they are at by the total mass of the system. The configurations considered in the paper vary upon the way we choose the positions in the configuration. In his senior project, Finn Hardy determined that the expected value of the center of mass of random configurations on the one-dimensional integer lattice *0, 1, ..., n* is equal to* n/2*, where a random configuration is obtained by randomly assigning to each *i* between *0* and *n* a mass of value *m* or *M*, with probability *p* and *1-p* respectively. In this project, I will propose a formula for the standard deviation of the center of mass of this lattice, as well as the expected value and the standard deviation of the center of mass in two other random configurations: the one-dimensional uniform case, where the positions are chosen uniformly from *0* to *1*, and the two-dimensional uniform case, where the angle *theta*, based on whom the *x* and *y* coordinates are calculated, is chosen uniformly from *0* to *2pi* on a unit circle. RStudio will be extensively used to create our database and statistically analyze obtained results. More complicated computations will be performed in Mathematica.

## Open Access Agreement

Open Access

## Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

## Recommended Citation

Nguyen, Thuy Linh, "Expected Value and Standard Deviation of the Center of Mass of Random Configurations" (2018). *Senior Projects Spring 2018*. 292.

https://digitalcommons.bard.edu/senproj_s2018/292

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