Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.3. Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Assume the following: Of the 63 robots with legs only, 50 have two legs, 5 have three legs, and 8 have four legs; of the 8 robots with both legs and wheels, all 8 have two legs. Suppose one of the 106 social robots is randomly selected. Let x equal the number of legs on the robot.

a. List the possible values of x.

b. Find the probability distribution of x.

c. Find E1x2 and give a practical interpretation of its value.