The LiDAR is an electro-optical machine designed to measure the distance and the velocity of the target possibly at every firing. Because the received signal is impaired by noise, the measurement of the target distance and its velocity must be considered stochastic processes. Accordingly, the LiDAR performance is quantified in terms of the probability of detection under given environmental conditions. In the noiseless case, the cross-correlation process between the received PRBS pattern and the reference PRBS pattern collapses upon a deterministic function and will always return a single peak corresponding to the distance of the target. However, noise unavoidably perturbs that ideal situation, generating some unpredictability of each cross-correlation outcome. The question now arises is: which is the probability that the highest peak of the cross-correlation outcome will coincide with the expected target distance? It should also be apparent that a larger noise will increase the uncertainty of the distance measurements and, definitely, will reduce the probability that the highest peak of the cross-correlation outcome will correspond to the expected target distance.