This probably isn't needed anymore, but I thought I'd give it a shot. First,
$$
\left\{x,p\right\} = \left[x,p\right] + 2 p x = i \hbar + 2 p x.
$$
So,
$$
\begin{eqnarray}
\left<\left\{\Delta x , \Delta p \right\}\right> &=& \left<\left\{x-\left<x\right>,p-\left<p\right>\right\}\right> \\
&=& \left<\left\{x,p\right\} - \left\{\left<x\right>,p\right\} - \left\{x,\left<p\right>\right\} + \left\{\left<x\right>,\left<p\right>\right\}\right> \\
&=& \left<\left\{x,p\right\}\right> - 2 \left<x\right> \left<p\right> - 2 \left<x\right> \left<p\right> + 2\left<x\right>\left<p\right> \\
&=& i \hbar + 2 \left(\left<p x\right> - \left<x\right> \left<p\right>\right) \\
&=& i \hbar + 2 \ cov\left(p,x\right)
\end{eqnarray}
$$
where the covariance of $p$ and $x$ is used in the last line.