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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 $𝑐_0,\ldots,c_3$. While standing in cell $𝑐_0$, the robot integrates four measurements $𝑧_{𝑡_0}, \ldots, z_{t_3}$. After integrating these measurements, the resulting belief of the robot with regards to the occupancy of the four cells is $𝑏_0 = 0.25$, $𝑏_1 = 1.3$, $𝑏_2 = 0.5$, $𝑏_3 = 1$. Given the three measurements $𝑧_{𝑡_0} = 0$, $𝑧_{𝑡_2} = 3$, $𝑧_{𝑡_3} = 1$, compute the value of the measurement $𝑧_{𝑡_1}$.

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    $\begingroup$ We seem to be missing some background here, which makes the question rather hard to answer. $\endgroup$ – Yuval Filmus Dec 13 '16 at 18:14
  • $\begingroup$ 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. $\endgroup$ – D.W. Dec 13 '16 at 23:12

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