# Likelihood field sensor model (Probabilistic Robotics, Thrun et al., p.169-174)

I am currently working on the "likelihood field" sensor model (aka "endpoint model") by Thrun et al. (book: Probabilistic Robotics, Thrun et al., p.169-174) In this context I have two questions. According to the authors, the probability of a sensor measurement zt^k can be described by a weighted set consisting of phit, prand and pmax (mixing weights zhit, zrand, zmax):

In the following, the authors describe that the implementation of the likelihood field algorithm (see below) does not take zmax measurements into account.

Question 1: If zmax measurements are rejected, what is the intention of the probability pmax in equation (6.34)?

My second question refers to line 8 of the following algorithm:

Note errata : replace "z_random" by "z_rand" (http://probabilistic-robotics.informatik.uni-freiburg.de/errata.html)

What is the meaning of the second term zrand/zmax? Does zrand describe the weight factor of the uniform distribution prand = 1/zmax? In this context, zmax describes the maximum range of the laser scanner and not a weight factor...