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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)鈥攁 formal language for representing, generating, and organizing variation in tree-structured artefacts. The CCC language was compared to two other coding languages鈥攖he 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

Expert verified

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

For two events, A and B, P(A)= .4, P(B)= .2 , and P(A鈭�B) = .1:

a. Find P (A/B).

b. Find P(B/A).

c. Are A and B independent events?

Shopping with a smartphone.Each year, United Parcel Service (UPS) commissions a 鈥淧ulse of the Online Shopper鈥� survey. The 2015 survey included a sample of 5,118 U.S. shoppers who have made at least two online purchases

every three months. The survey revealed that 41% of the shoppers used a smartphone to make a purchase. Of those who made a smartphone purchase, 38% indicated that they preferred the mobile Web site to the full Web site accessed through a computer. Assume these percentages represent actual probabilities for the population of online shoppers. What is the probability that a randomly selected online shopper uses a smartphone to make a purchase and

prefers the mobile Web site?

Stock market participation and IQ.Refer to The Journal of Finance(December 2011) study of whether the decisionto invest in the stock market is dependent on IQ, Exercise3.46 (p. 182). The summary table giving the number ofthe 158,044 Finnish citizens in each IQ score/investment category is reproduced below. Again, suppose one of the citizens is selected at random.

IQ Score

Invest in Market

No Investment

Totals

1

2

3

4

5

6

7

8

9

893

1,340

2,009

5,358

8,484

10,270

6,698

5,135

4,464

4,659

9,409

9,993

19,682

24,640

21,673

11,260

7,010

5,067

5,552

10,749

12,002

25,040

33,124

31,943

17,958

12,145

9,531

Totals

44,651

113,393

158,044

Source:Based on M. Grinblatt, M. Keloharju, and J. Linnainaa, 鈥淚Q and Stock Market Participation,鈥� The Journal of Finance, Vol. 66, No. 6, December 2011 (data from Table 1 and Figure 1).

a.Given that the Finnish citizen has an IQ score of 6 or higher, what is the probability that he/she invests in the stock market?

b.Given that the Finnish citizen has an IQ score of 5 or lower, what is the probability that he/she invests in the stock market?

c.Based on the results, parts a and b, does it appear that investing in the stock market is dependent on IQ? Explain.

Condition of public school facilities. The National Center for Education Statistics (NCES) conducted a survey on the condition of America鈥檚 public school facilities. The survey revealed the following information. The probability that a public school building has inadequate plumbing is .25. Of the buildings with inadequate plumbing, the probability that the school has plans for repairing the building is .38. Find the probability that a public school building has inadequate plumbing and will be repaired.

Who prepares your tax return? As part of a study on income tax compliance (Behavioral Research and Accounting, January 2015), researchers sampled 270 adults at a shopping mall and asked each: 鈥淲ho usually prepares your tax return?鈥� Their answers (and frequency of responses) are shown in the table (p. 170). Use the information in the table to estimate the probability that a randomly selected adult uses a friend, relative, or professional to prepare his or her income tax return.

Table for Exercise 3.16

Response

Frequency

You

100

Your spouse

16

Equally with spouse

7

Friend or relative

31

Professional help

114

Not required to file

2

TOTAL

270

Source: S. Bhattacharjee, K. Moreno, and D. Salbador, 鈥淭he Impact of Multiple Tax Returns on Tax Compliance Behavior,鈥� Behavioral Research and Accounting, Vol. 27, No. 1, January 2015 (from Table 1).
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