# Using counting to build a grid world

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 $π_0,\ldots,c_3$. While standing in cell $π_0$, the robot integrates four measurements $π§_{π‘_0}, \ldots, z_{t_3}$. After integrating these measurements, the resulting belief of the robot with regards to the occupancy of the four cells is $π_0 = 0.25$, $π_1 = 1.3$, $π_2 = 0.5$, $π_3 = 1$. Given the three measurements $π§_{π‘_0} = 0$, $π§_{π‘_2} = 3$, $π§_{π‘_3} = 1$, compute the value of the measurement $π§_{π‘_1}$.

• We seem to be missing some background here, which makes the question rather hard to answer. – Yuval Filmus Dec 13 '16 at 18:14
• What's the source of this exercise? We expect you to credit your sources, especially when quoting material written by others in your question. See our guidelines on using and referencing material written by others: cs.stackexchange.com/help/referencing. – D.W. Dec 13 '16 at 23:12