## Senior Projects Spring 2018

Spring 2018

Mathematics

Amir Barghi

Japheth Wood

#### Abstract/Artist's Statement

Let $G$ be a simple graph and $m, M$ be positive reals. Suppose we have a coin that when flipped the probability of heads (H) is $p$ and the probability of tails (T) is $1-p$, where $p \in [0,1]$. For each vertex in $G$, we flip the coin. If the outcome is H, we place a mass of size $M$ at that vertex; otherwise, we place a mass of size $m$. For each edge $e$ in $G$, let $Y_e$ be a function of the masses of its endpoints, for example, the average masses of its endpoints. In words, let $Y_G$ be the sample mean of $Y_e$ as $e$ ranges across the edges of graph $G$. We study the expectation and variance of $Y_G$ for different families of graphs.

On-Campus only