Refer to Exercise 6.6. Are X and Y independent?

Data from Exercise 6.6

Refer to The International Journal of Robotics Research (Dec. 2004) study of a robot-sensor system in an unknown environment. 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 A ↔ B the 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.