We derive the additive property of Poisson random variables directly from the probability mass function. An important application of the additive property to quality testing of computer chips is presented.

An agreement table with [n as an element of N is greater than or equal to] 3 ordered categories can be collapsed into n - 1 distinct 2 x 2 tables by combining adjacent categories. Vanbelle and Albert ("Stat. Methodol." 6:157-163, 2009c) showed that the components of Cohen's weighted kappa with linear weights can be obtained from these n - 1…

The linear regression model is one of the most popular models in statistics. It is also one of the simplest models in statistics. It has received applications in almost every area of science, engineering and medicine. In this article, the authors show that adding a predictor to a linear model increases the variance of the estimated regression…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…

North Korea is one of the most closed nations in the world. It is difficult to access information about their education system. North Korea's economic system was reorganized on July 1, 2002, as well as the education system. This change has impacted North Korea's mathematics education. With limited information on North Korean mathematics textbooks,…

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…

It is very well known that the Cauchy-Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy-Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real…

This note introduces an interesting random walk on a straight path with cards of random numbers. The method of recurrent relations is used to obtain the convergent probability of the random walk with different initial positions.

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…