Robot–sensor system configuration. Engineers at Broadcom Corp. and Simon Fraser University...

Robot–sensor system configuration. Engineers at Broadcom Corp. and Simon Fraser University collaborated on research involving a robot–sensor system in an unknown environment (The International Journal of Robotics Research, Dec. 2004). As an example, the engineers presented the three–point, single–link robotic system shown in the accompanying figure. Each point (A, B, or C) in the physical space of the system has either an “obstacle” status or a “free” status. There are two single links in the system: A↔B and B↔C. A link has a “free” status if and only if both points in the link are “free”; otherwise the link has an “obstacle” status. Of interest is the random variable x: the total number of links in the system that are “free.”

a. List the possible values of x for the system.

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b. The researchers stated that the probability of any point in the system having a “free” status is .5. Assuming that the three points in the system operate independently, find the probability distribution for x.