• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.147-153
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• 2010

It is generally believed that teaching probability with the help of coin tossing has a long history. In textbooks about elementary probability or statistics, problems on unfair coins as well as fair ones are frequently given. However it is known that nobody has met an unfair coin with a fixed head probability which is different from 0.5 in flesh and blood. In this study a coin bent along with the middle line of the coin is suggested as an unfair one. By flipping bent coins with various angle, the ratios of head of the coins are obtained. The bent coins might be used as experimental tools for teaching of probability concept.

• Structural Engineering and Mechanics
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• v.57 no.1
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• pp.21-43
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• 2016

A conditional probability based approach known as Particle Filter Method (PFM) is a powerful tool for system parameter identification. In this paper, PFM has been applied to identify the vehicle parameters based on response statistics of the bridge. The flexibility of vehicle model has been considered in the formulation of bridge-vehicle interaction dynamics. The random unevenness of bridge has been idealized as non homogeneous random process in space. The simulated response has been contaminated with artificial noise to reflect the field condition. The performance of the identification system has been examined for various measurement location, vehicle velocity, bridge surface roughness factor, noise level and assumption of prior probability density. Identified vehicle parameters are found reasonably accurate and reconstructed interactive force time history with identified parameters closely matches with the simulated results. The study also reveals that crude assumption of prior probability density function does not end up with an incorrect estimate of parameters except requiring longer time for the iterative process to converge.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.77-87
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• 2015

Parrondo paradox is the counter-intuitive phenomenon where two losing games can be combined to win or two winning games can be combined to lose. In this paper, we consider an ensemble of players, one of whom is chosen randomly to play game A' or game B. In game A', the randomly chosen player transfers one unit of his capital to another randomly selected player. In game B, the player plays the history-dependent Parrondo game in which the winning probability of the present trial depends on the results of the last two trials in the past. We show that Parrondo paradox exists in this redistribution model of the history-dependent Parrondo game.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.737-752
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• 2008

About 1800, mathematicians combined analysis of error and probability theory into error theory. After developed by Gauss and Laplace, error theory was widely used in branches of natural science. Motivated by the successful applications of error theory in natural sciences, scientists like Adolph Quetelet tried to incorporate social statistics with error theory. But there were not a few differences between social science and natural science. In this paper we discussed topics raised then. The problems considered are as follows: the interpretation of individual man in society; the arguments against statistical methods; history of the measures for diversity. From the successes and failures of the $19^{th}$ century social statisticians, we can see how statistics became a science that is essential to both natural and social sciences. And we can see that those problems, which were not easy to solve for the $19^{th}$ century social statisticians, matter today too.

• Journal of the Korean School Mathematics Society
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• v.3 no.1
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• pp.59-67
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• 2000

This study has been done to help teach mathematics on the spot of education by providing the history of mathematics and illustrations concerning mathematics, which were rearranged for the level of the second grade students in highschool and intented to interest students in mathematics classes. The contents of teaching, according to each unit (Matrix, Sequence, Limit, Differentiation, Integration, Probability, Statistics) include the life of the representative mathematician, the historical background centered on episodes, questions linked with reality, questions making sensations in history and something for maxim in mathematics. If such contents are properly used, they are expected to be able to stimulate students' curiosity, and to be effective in improving students' learning ability in mathematics by causing them to show their active attitudes toward learning mathematics.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.745-753
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• 2014

Parrondo paradox is the counter-intuitive situation where individually losing games can combine to win or individually winning games can combine to lose. In this paper, we compare the history-dependent Parrondo games and the space-dependent Parrondo games played cooperatively by the multiple players. We show that there is a probability region where the history-dependent Parrondo game is a losing game whereas the space-dependent Parrondo game is a winning game.

• The Mathematical Education
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• v.42 no.4
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• pp.453-463
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• 2003

The main purpose of this paper is to develope elementary mathematics teaching-learning programs for pre-service elementary teachers. The elementary mathematics education program developed in this work is divided into two parts: One is the theory, the other is the practice. The theory deals with the foundations of mathematics, the objectives of mathematics education, the history of mathematics education in Korea, the psychology of mathematics learning, the theories of mathematics teaching and learning, and the methods of assessment. With respect to the practice, this study examines the background knowledge and activities of numbers and their operation, geometry, measurement, statistics and probability, pattern and function.

• Journal for History of Mathematics
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• v.32 no.2
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• pp.61-77
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• 2019

The study was conducted based on the 'method of mathematical exploration through history'. In recent school education, 'Probability and Statistics' education has been emphasized, and as a result, the study has conducted a study on permutations. Permutation is used in a variety of fields, and in this study, we looked at the Derangement. The results of this study are as follows. First, analysis was made at current school mathematics level and academic mathematics level for Derangement. Second, the historical development process of derangement was examined. Third, based on this, the research direction of this study was decided to be 'Derangement number's triangle(Rencontres number's triangle)', and the inquiry for education expansion was carried out. Fourth, we have presented data on concrete educational expansion by discovering various mathematical facts of the Derangement number's triangle. We hope that the results of this study will provide meaningful implications for the application of mathematics and the presentation of new inquiry directions.

• Journal for History of Mathematics
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• v.37 no.1
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• pp.1-17
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• 2024

In this study, we identified the intellectual triggers for Bayesian inference and what key ideas contributed to its occurrence and discussed the practical implications of introducing Bayesian inference into the school mathematics curriculum by reflecting them. The results of the study show that the need for statistical inference about the parameter itself served as a trigger for the occurrence of Bayesian inference, and the most important idea for the occurrence of that inference was to regard the parameter itself as a probability variable rather than any fixed value. On the other hand, these research results suggest that the meaning of introducing Bayesian inference into the secondary mathematics curriculum is 'statistics education that expands the scope of uncertainty'.

• Journal of the Korean Data and Information Science Society
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• v.22 no.4
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• pp.631-641
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• 2011

We consider a history-dependent Parrondo game in which the winning probability of the present trial depends on the results of the last two trials in the past. When a fraction of an infinite number of players are allowed to choose between two fair Parrondo games at each turn, we compare the blind strategy such as a random sequence of choices with the short-range optimization strategy. In this paper, we show that the random sequence of choices yields a steady increase of average profit. However, if we choose the game that gives the higher expected profit at each turn, surprisingly we are not supposed to get a long-run positive profit for some parameter values.