The treatment of kurtosis in textbooks is both sparse and contradictory with applications rarely discussed. To address this, an easily understood definition of kurtosis is introduced and important applications are demonstrated. Two different approaches to teaching kurtosis are presented based on a financial application.

We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…

In this article an application of conformal mapping to aerofoil theory is studied from a geometric and calculus point of view. The problem is suitable for undergraduate teaching in terms of a project or extended piece of work, and brings together the concepts of geometric mapping, parametric equations, complex numbers and calculus. The Joukowski…

In this note the Nearest Neighbour Index is investigated in three cases, linear, 2-dimensional and 3-dimensional. In each case the formula is investigated and the numerical values for the data points to be viewed as attracting each other, repelling each other or being randomly distributed are justified. Also, in each of the three cases mentioned…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

The mean and variance of some continuous distributions, in particular the exponentially decreasing probability distribution and the normal distribution, are considered. Since they involve integration by parts, many students do not feel comfortable. In this note, a technique is demonstrated for deriving mean and variance through differential…

In this issue's "Classroom Notes" section, the following papers are described: (1) "Sequences of Definite Integrals" by T. Dana-Picard; (2) "Structural Analysis of Pythagorean Monoids" by M.-Q Zhan and J. Tong; (3) "A Random Walk Phenomenon under an Interesting Stopping Rule" by S. Chakraborty; (4) "On Some Confidence Intervals for Estimating the…