# TEACHING BINOMIAL AND POISSON DISTRIBUTIONS IN AN UNDERGRADUATE ENGINEERING COURSE

C. CapillaPolytechnic University of Valencia (SPAIN)

The aim of this paper is to discuss the teaching of theBinomial and Poisson probability distributions in an undergraduate Computer Science Engineering degree. Seven groups of students are considered (sample size 292). They were in the second semester of the degree. Three groups followed the course in the academic year 2013_14, and the other four in 2014_15. In two groups of the first year and in another two of the second one, the basic concepts of these discrete distributions were explained in two classroom lectures of 90 minutes. The main goals were teaching students to calculate specific probabilities and to apply several mathematical equations. The distributions theoretical definitions were introduced. Some examples of random variables illustrated the models. The cumulative probability and mass functions were presented. These models dependence on their parameters was graphically illustrated using statistical software. The Binomial equation was applied in an attribute quality control exercise. The acceptance probability of a sampling plan from a batch was computed, considering a given sample size, and a criterion to decide its acceptability. The Poisson model was applied to obtain probabilities in two examples of other contexts. The calculations were done with the mass distribution formula, and a plot of the cumulative probability curves. In both distributions, the probabilities were also obtained using the statistical software. The formulas to compute the Binomial distributions central location and dispersion measures (mean and variance) were introduced, as well as their application to some examples. In the other three groups that are considered in this work , the classroom lectures had a different approach. Several assessment activities evaluated studentsâ€™ instrumental understanding of all these concepts during the course. One of them was done in the last part of the computer laboratory session, which lasted 90 minutes, and was evaluated by the same teacher. The seven groups were divided in two subgroups. In the first part of the practice, two or four attribute quality control problems were explained depending on the group. These problems were similar to the exercises introduced in the classroom lectures, and required the application of the Binomial and Poisson models. The sample sizes were obtained for required acceptability/rejection criteria and probabilities. Computations were made by hand (Binomial distribution) and with the plot of the Poisson cumulative probability curves. In the next session of the practice, students used statistical software to plot the Binomial mass and cumulative distribution functions, and computed their values on different numbers of defective units of an exercise. They also applied the software to calculate Poisson distribution probabilities. They worked in teams of two or three people. In the evaluation they presented a consensus written answer to a problem similar to the ones included in the first part of the practice. The practice evaluationâ€™s average marks are analyzed to study differences between groups and years.