E1.7 Random Robot Motions on a Roadmap, part III (15 points). In this problem you will program a histogram filter over the factory locations. Follow the following steps: (i) (5 points) Write a function cutr_belief_update(belx,u), which takes as an input an arbitrary vector of control commands , for t = 1, 2, ..., T, taking values (ut = 1) and (ut = 0)), and a belief vector belx on the location of the robot at a certain time (). This function should output the updated belief at time T. (ii) (5 points) Write a function mes_belief_update(belx,z) which takes as an input an arbitrary vector of measurements 2, for t = 1, 2,...T, and the belief vector on the location of the robot at a certain time (), belx. The set of measurements can refer to any node in the graph (e.g. z E {'A',' B'!' C',' D'}) or, if no measurement was taken z = 0. This function then outputs the corrected belief on the robot location at time T. (iii) (5 points) Finally, using the previous two functions, write a third function belief_update(belx,u,z), which takes as an input the sequence of z's, the sequence of u's, (of any length 7), and initial belief vector, belx, on the location of the robot. The function should output the final belief vector on the location of the robot at time T