The objectives of the CEMERLL experiment are to measure the signal enhancement obtained in a two way laser propagation link using laser guidestar adaptive optics from the Earth to the Moon using the Apollo retroreflector arrays, and to predict and verify the resulting signal strength and variability. A theory is presented for the probability density functions of the laser link by combining multiple effects of the: 1) compensated laser uplink through turbulence, 2) reflection from the lunar retroreflector array, 3) passage through turbulence on the downlink, aperture averaging by the receiving telescope, and 4) signal detection with a photovoltaic detector. The most important element in the chain is the uplink propagation, all other effects propagation effects modify only the mean number of photons of this two way link, and do not significantly change the probability density functions of the uplink laser beam. The resulting probability density functions are defined by parameters that include the effective number of scatterers, the average intensities in the specular and diffuse portions of the beam, and the beam jittering effect of using a laser guidestar. Using intensity moments derived from the far field propagation, performance data on the laser guidestar adaptive optics system, and approximations for higher order moments, the parameters of these distributions can be numerically evaluated from experimental conditions. These show a widely diffuse speckle pattern for the uncompensated beam, and a similar shaped but long tailed distribution for the compensated beam. Uncorrected tilt effects cause the well compensated beam to randomly jitter and results in an intensity distribution where there are some 'hits' of high intensity light, but more frequently there is a portion of the beam side lobes which illuminate the corner cube array. A separate tip-tilt correction using either an illuminated lunar feature or the return pulses themselves would mitigate this effect.