For this question, I have tried everything that I can think of, but cannot solve it. What I want to do is iterate over all possible values of $z_1$, but every method I use, it requires me to know what $p(m|z_1)$ will be for various $z_1$ values. Thus I am stumped and looking for help.
A robot applies the so-called simple counting approach to build a grid map of a 1D environment consisting of the cells $_0,\ldots,c_3$. While standing in cell $_0$, the robot integrates four measurements $_{_0}, \ldots, z_{t_3}$. After integrating these measurements, the resulting belief of the robot with regards to the occupancy of the four cells is $_0 = 0.25$, $_1 = 1.3$, $_2 = 0.5$, $_3 = 1$. Given the three measurements $_{_0} = 0$, $_{_2} = 3$, $_{_3} = 1$, compute the value of the measurement $_{_1}$.
