You are designing a new robot to give campus tours. but while testing the robot in aldrich park, it malfunctions and begins driving randomly along a path. let x = 0 indicate the robot’s position when the malfunction occurs, positive x values indicate movement to the north, and negative x values indicate movement to the south.
a) suppose that every minute, the robot travels south 5 meters with probability 1/2, or north 5 meters with probability 1/2. the directions of travel at successive minutes are indepen- dent. after one hour, what is the expected position of the robot? what is the standard deviation of the robot’s position?
b) suppose instead that the motor controllers on the robot are biased, so that every minute it travels south 5 meters with probability 3/4, or north 5 meters with probability 1/4. the directions of travel at successive minutes are independent. after one hour, what is the expected position of the robot? what is the standard deviation of the robot’s position?
c) you were taking a break when the robot began malfunctioning, and did not observe its movement. under which motion model, the one from part (a) or part (b), do you think it would be faster to find your lost robot? justify your answer.