\begin{problem}[10]
Let $G_1, \dots, G_n, \dots$ be independent variables with the same
distribution and the same expectation, $\mu$, and let
\[
f(n, \epsilon) \eqdef \pr{\abs{\frac{\sum_{i=1}^n G_i}{n} - \mu} \leq \epsilon}.
\]
The Weak Law of Large Numbers can be expressed as a logical formula of
the form:
\[
\forall \epsilon > 0\,Q_1\,Q_2\dots\, [f(n,\epsilon) \geq 1 - \delta]
\]
where $Q_1Q_2\dots$ is a sequence of quantifiers from among:
\begin{itemize}
\item $\forall n_0$
\item $\forall n \geq n_0$
\item $\forall \delta > 0$
\item $\forall \delta \geq 0$
\item $\exists n_0$
\item $\exists n \geq n_0$
\item $\exists \delta \geq 0$
\item $\exists \delta >0$
\end{itemize}
Here the $n$ and $n_0$ range over natural numbers, and $\delta$ and
$\epsilon$ range over real numbers.

Write out the proper sequence $Q_1Q_2\dots$ \brule{3in}

\solution{$\forall \epsilon > 0 \, \forall \delta > 0\, \exists n_0\,
\forall n \geq n_0$}

\end{problem}
