The Law of Large Numbers ◾ 179
Exercises
1. In a certain school, it has been estimated that the probability of students pass-
ing mathematics tests is 69%. Find out the probability of at least 80 passes
in a batch of 89 students. Plot the related binomial distribution. Use Excel
function BINOM.DIST for your calculations.
2. In a certain application 12 modules have just been built. Test results show that
there are 4 defective modules. If we draw samples of size 3 without replace-
ment, find the probability that a sample contains two defective modules. Use
the Excel function HYPGEOM.DIST for your calculations.
3. Right first-time design probability in a software development project is esti-
mated at 0.3. Estimate the probability of needing seven trials to find a defect-
free feature design. Plot a graph between trials and geometric probability.
References
1. B. Singh, R. Viveros and D. L. Parnas, Estimating Software Reliability Using Inverse Sampl ing,
Communications Research Laboratory, McMaster University, Hamilton Department
of Mathematics and Statistics, e College of Information Sciences and Technology,
e Pennsylvania State University. Available at http://citeseerx.ist.psu.edu/viewdoc
/download?doi=10.1.1.71.1577&rep=rep1&type=pdf.
2. M. Wisal, Formal Verification of Negative Binomial Distribution in Higher Order Logic,
Department of Computer Engineering, University of Engineering and Technology,
Taxila, 2012.
3. D. R. Bellhouse, e Reverend omas Bayes, FRS: A biography to celebrate the ter-
centenary of his birth, Statistical Science, 19(1), 3–43, 2004.
4. T. Lohrbeer, Bayesian Maths for Dummies. Available at http://blog.fastfedora.com
/2010/12/bayesian-math-for-dummies.html.
5. S. Chulani, B. Boehm and B. Steece, Bayesian Analysis of Empirical Software Engineering Cost
Models, University of Southern California, IEEE Transactins on Software Engineering,
USC-CSE, 1999.
6. N. Fenton, Software Project and Quality Modelling Using Bayesian Networks. Available
at http://www.eecs.qmul.ac.uk/~norman/papers/software_project_quality.pdf.
7. S. Bibi, I. Stamelos and L. Angelis, Bayesian Belief Networks as a Software Productivity Esti-
mation Tool, Department of Informatics, Aristotle University, essaloniki, Greece, 2003.
8. S. Wagner, A Bayesian network approach to assess and predict software quality using
activity-based quality models. In: Proceeding PROMISE ‘09 Proceedings of the 5th
International Conference on Predictor Models in Software Engineering, Article No. 6,
ACM, New York, 2009.
Suggested Reading
Wroughton, J. and T. Cole, Distinguishing between binomial, hypergeometric and negative
binomial distributions, Journal of Statistics Education, 21(1), 2013. Available at http://
www.amstat.org/publications/jse/v21n1/wroughton.pdf.