1 . Let $G = (V,E)$ be a graph with vertex set $V$ and edge set $E$, let $n$ be the size of $V$, and let $m$ be the size of $E$. For each vertex of $V$, flip a fair and independent coin. Let $V'$ be the subset of $V$ consisting of all vertices of $V$ whose coin flip resulted in heads. Let $E'$ be the set consisting of all edges $(u,v)$ in $E$ for which both $u$ and $v$ are in $V'$. Define the random variable $X$ to be the number of edges in $E'$. What is the expected value of $X$?