$$A_{average} =
\frac{\int_{-\infty}^{\infty} A(p,q) \ e^{-\frac{E}{kT} }dp\,dq}
{\int_{-\infty}^{\infty} e^{-\frac{E}{kT} }dp\,dq}\quad ?$$
Yes I meant this indeed.
So I'm viewing it as follows:
p = $$(p_{x1}, p_{y1}, p_{z1} ; p_{x2}, p_{y2}, p_{z2}... p_{xN}, p_{yN}...