Question

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 (p. 72). 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.

1. List the possible values of x.
2. Find the probability distribution of x.
3. Find $\mathbf{\text{E}}\mathbf{\left(}\mathbf{\text{x}}\mathbf{\right)}$and give a practical interpretation of its value.

Short answer

a. x = (Two legs, three legs, four legs, and wheels, no legs)

b.The image is given below:

c. 36.58

Step-by-step solution

(a) Definition of random selection

Random selection mainly refers to selecting something randomly by a researcher from a large number of sample units. In statistics, this thing is applicable while conducting any statistical test.

Finding the possible values

Since there are four types of robots, there can be four values of x.The values are the robots with two legs, robots with three legs, robots with four legs, the robots with two legs and wheels, and the robots without legs.

(b) Values of x

The possible values of x, which represent the type of robots, are shown below:

$\mathbf{\text{x=}}\mathbf{\left(}\mathbf{\text{Two\hspace{0.17em}legs,\hspace{0.17em}three\hspace{0.17em}legs,\hspace{0.17em}four\hspace{0.17em}legs,\hspace{0.17em}legs\hspace{0.17em}and\hspace{0.17em}wheels,nolegs\hspace{0.17em}}}\mathbf{\right)}$

Computation of the probability distribution

The total number of robots of a specific type is listed below, along with the associated probability distribution:

(c) Calculation of E(x)

The possible values of x, which represent the type of robots, are shown below:

$\begin{array}{c}\mathbf{\text{E}}\mathbf{\left(}\mathbf{\text{x}}\mathbf{\right)}\mathbf{\text{=Numberofrobotswithtwolegs}}\mathbf{\left(}\mathbf{\text{associated\hspace{0.17em}probability}}\mathbf{\right)}\\ \mathbf{\text{+Numberofrobotswiththreelegs}}\mathbf{\left(}\mathbf{\text{associated\hspace{0.17em}probability}}\mathbf{\right)}\\ \mathbf{\text{+Numberofrobotswithfourlegs}}\mathbf{\left(}\mathbf{\text{associated\hspace{0.17em}probability}}\mathbf{\right)}\\ \mathbf{\text{+Numberofrobotswithtwolegsandwheels}}\mathbf{\left(}\mathbf{\text{associated\hspace{0.17em}probability}}\mathbf{\right)}\\ \mathbf{\text{+Numberofrobotswithnolegs}}\mathbf{\left(}\mathbf{\text{associated\hspace{0.17em}probability}}\mathbf{\right)}\\ \mathbf{\text{=50}}\mathbf{\left(}\mathbf{\text{0.47}}\mathbf{\right)}\mathbf{\text{+5}}\mathbf{\left(}\mathbf{\text{0.05}}\mathbf{\right)}\mathbf{\text{+8}}\mathbf{\left(}\mathbf{\text{0.08}}\mathbf{\right)}\mathbf{\text{+8}}\mathbf{\left(}\mathbf{\text{0.08}}\mathbf{\right)}\mathbf{\text{+35}}\mathbf{\left(}\mathbf{\text{0.33}}\mathbf{\right)}\\ \mathbf{\text{=36.58}}\end{array}$

Interpretation of E(x)

36.58 is the calculated mean calculated in step 1, but it has a certain interpretation.The value of 36.58 indicates that the researcher will pick up 37.58 robots with legs.