Robot-sensor system configuration. Refer to The International Journal of Robotic

Question

Robot-sensor system configuration. Refer to The International Journal of Robotics Research (Dec. 2004) study of a robot-sensor system in an unknown environment, Exercise 4.5 (p. 122). In the three-point, single-link robotic system shown in the accompanying figure, each point (A, B, or C) in the system has either an "obstacle" status or a "free" status. Let X = 1 if the A B link has an "obsta­cle" and X = 0 if the link is "free" (i.e., has no obstacles). Similarly, let Y = 1 if the B C link has an "obstacle" and Y = 0 if the link is "free." Recall that the researchers assumed that the probability of any point in the system having a "free" status is .5 and that the three points in the system operate independently. Give p(x, y), the joint probability distribution of X and Y, in table form. Find the conditional probability distribution, p1(x y). Find the marginal probability distribution, p1(x).

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