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Chapter 3: Q3-51E (page 183)

Encoding variability in software. At the 2012 Gulf Petrochemicals and Chemicals Association (GPCA) Forum, Oregon State University software engineers presented a paper on modelling and implementing variation in computer software. The researchers employed the compositional choice calculus (CCC)—a formal language for representing, generating, and organizing variation in tree-structured artefacts. The CCC language was compared to two other coding languages—the annotative choice calculus (ACC) and the computational feature algebra (CFA). Their research revealed the following: Any type of expression (e.g., plain expressions, dimension declarations, or lambda abstractions) found in either ACC or CFA can be found in CCC; plain expressions exist in both ACC and CFA; dimension declarations exist in ACC, but not CFA; lambda abstractions exist in CFA, but not ACC. Based on this information, draw a Venn diagram illustrating the relationships among the three languages. (Hint: An expression represents a sample point in the Venn diagram.)

Short Answer

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Answer

Fig.1 Venn diagram (shown in step 2)

Step by step solution

01

Step-by-Step SolutionStep 1: Introduction

A Venn diagram is a probability diagram with one or more circles inside a rectangle and demonstrates logical relationships between occurrences. In a diagram, the rectangle symbolizes the sample space or the universal set, which collects all possible outcomes. A circle within a rectangle symbolizes an event, i.e., a subset of the sample space.

02

Venn diagram shows the relationship among the languages

The above Venn diagram shows that the CCC (Compositional Choice Calculus) language was compared to two other coding languages: ACC and CFA. They exist in:

  1. ACC (Annotative Choice Calculus) exist in dimension declaration.
  2. CFA (Computational Feature Algebra) exist in lambda abstraction.
  3. Both the languages ACC and CFA have existed in plain expression.

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Most popular questions from this chapter

Wine quality and soil.The Journal of Wine Research(Vol.21, 2010) published a study of the effects of soil and climate on the quality of wine produced in Spain. The soil at two vineyards— Llarga and Solar—was the focus of the analysis.Wine produced from grapes grown in each of the two vineyards

was evaluated for each of three different years (growing seasons) by a wine-tasting panel. Based on the taste tests, the panel (as a group) selected the wine with the highest quality.

a.How many different wines were evaluated by the panel, where one wine was produced for each vineyard/growing season combination?

b.If the wines were all of equal quality, what is the probability that the panel selected a Llarga wine as the wine with the highest quality?

c.If the wines were all of equal quality, what is the probability that the panel selected a wine produced in year 3 as the wine with the highest quality?

d.The panel consisted of four different wine tasters who performed the evaluations independently of each other. If the wines were all of equal quality, what is the probability that all four tasters selected a Llarga wine as the wine with the highest quality?

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 3.10 (p. 168). Recall that in a random sample of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Use the complements rule to find the probability that a randomly selected social robot is designed with either legs or wheels.

Profile of a sustainable farmer. Sustainable development or sustainable farming means finding ways to live and workthe Earth without jeopardizing the future. Studies wereconducted in five Midwestern states to develop a profileof a sustainable farmer. The results revealed that farmerscan be classified along a sustainability scale, dependingon whether they are likely (L) or unlikely (U) to engagein the following practices: (1) raise a broad mix of crops;(2) raise livestock; (3) use chemicals sparingly; and (4) usetechniques for regenerating the soil, such as crop rotation.

  1. List the different sets of classifications that are possible for the four practices (e.g., LUUL).
  2. Suppose you plan to interview farmers across the country to determine the frequency with which they fall into the classification sets you listed for part a. Because no information is yet available, assume initially that there is an equal chance of a farmer falling into any single classification set. Using that assumption, what is the probability that a farmer will be classified as unlikely on all four criteria (i.e., classified as a non-sustainable farmer)?
  3. Using the same assumption as in part b, what is the probability that a farmer will be classified as likely on at least three of the criteria (i.e., classified as a near sustainable farmer)?

On-the-job arrogance and task performance. Human Performance (Vol. 23, 2010) published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit arrogant behaviors on the job and that 10% of all full-time workers will receive a poor performance rating. Also, assume that 5% of all full-time workers exhibit arrogant behaviors and receive a poor performance rating. Let A be the event that a full-time worker exhibits arrogant behavior. Let B be the event that a full-time worker will receive a poor performance rating.

a. Are the events A and B mutually exclusive? Explain.

b. Find P(B/A).

c. Are the events A and B independent? Explain.

The three-dice gambling problem. According toSignificance(December 2015), the 16th-century mathematician Jerome Cardan was addicted to a gambling game involving tossing three fair dice. One outcome of interest— which Cardan called a “Fratilli”—is when any subset of the three dice sums to 3. For example, the outcome {1, 1, 1} results in 3 when you sum all three dice. Another possible outcome that results in a “Fratilli” is {1, 2, 5}, since the first two dice sum to 3. Likewise, {2, 3, 6} is a “Fratilli,” since the second die is a 3. Cardan was an excellent mathematician but calculated the probability of a “Fratilli” incorrectly as 115/216 = .532.

a. Show that the denominator of Cardan’s calculation, 216, is correct. [Hint: Knowing that there are 6 possible outcomes for each die, show that the total number of possible outcomes from tossing three fair dice is 216.]

b. One way to obtain a “Fratilli” is with the outcome {1,1, 1}. How many possible ways can this outcome be obtained?

c. Another way to obtain a “Fratilli” is with an outcome that includes at least one die with a 3. First, find the number of outcomes that do not result in a 3 on any of the dice. [Hint: If none of the dice can result in a 3, then there are only 5 possible outcomes for each die.] Now subtract this result from 216 to find the number of outcomes that include at least one 3.

d. A third way to obtain a “Fratilli” is with the outcome {1, 2, 1}, where the order of the individual die outcomes does not matter. How many possible ways can this outcome be obtained?

e. A fourth way to obtain a “Fratilli” is with the outcome {1, 2, 2}, where the order of the individual die outcomes does not matter. How many possible ways can this outcome be obtained?

f. A fifth way to obtain a “Fratilli” is with the outcome {1, 2, 4}, where the order of the individual die outcomes does not matter. How many possible ways can this outcome be obtained? [Hint:There are 3 choices for the first die, 2 for the second, and only 1 for the third.]

g. A sixth way to obtain a “Fratilli” is with the outcome {1, 2, 5}, where the order of the individual die outcomes does not matter. How many possible ways can this outcome be obtained? [See Hintfor part f.]

h. A final way to obtain a “Fratilli” is with the outcome {1, 2, 6}, where the order of the individual die outcomes does not matter. How many possible ways can this outcome be obtained? [See Hintfor part f.]

i. Sum the results for parts b–h to obtain the total number of possible “Fratilli” outcomes.

j. Compute the probability of obtaining a “Fratilli” outcome. Compare your answer with Cardan’s.
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