\begin{align*}
E\left( C \right) & = \sum_{i = 1}^{n - 1} E \left( C_i \right) = (n - 1) E \left( C_i \right) = (n - 1) \frac{1}{2} \\
D\left( C \right) & = \frac{1}{12} (n + 1)
\end{align*}