Many different properties of the positron containing systems PsH, [Li,e(+)], LiPs, and [LiH,e(+)], were computed using both variational Monte Carlo and fixed node diffusion Monte Carlo methods, and explicitly correlated trial wave functions. Our results show that these techniques can accurately compute not only energy values, but also other observables. Our [delta(r(+-))] values for PsH, [Li,e(+)], and LiPs are in good agreement with the most recent state of the art correlated calculations, while for [LiH,e(+)] our calculations are the first to give reliable results.