Positioning is a fundamental issue for wireless sensor network operation. Despite the recent proposals for the development of localization algorithms, the probabilistic behavior in position estimation using inaccurate measurements has not been analyzed. The paper focuses on two theoretical problems of localization from the viewpoint of probability analysis. First, it was proved that the position error in positioning is distributed by the χ2. Secondly, we demonstrated that the sensor connectivity distribution converges to the Poisson. Experiments of connectivity distribution were performed, and some conclusions were given to conduct a sensor network deployment.