• Research in Mathematical Education
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• 제15권2호
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• pp.127-140
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• 2011

"Statistical literacy" is important to be an effective citizen ([Gal, I. (2005). Towards "probability literacy" for all citizens: Building blocks and instructional dilemmas. In: G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 39-63). New York: Springer]). Probability and statistics has been connected with real context and can be used to stimulate students' creative abilities. This study aims at identifying the extent that textbooks in three countries include experimental probability concepts and non-routine, open-ended, application and contextual problems. How well textbooks reflect real application situations is important in the sense that students can employ probability concepts when solving real world problems. Results showed that three textbook series did not mention experimental probability. Furthermore, all of text-books had more routine, close-ended, knowing, and non-contextual problems.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권11호
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• pp.3638-3654
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• 2014

Cognitive Radio (CR) users need to sense the environment or channel at regular time interval for sharing the spectrum band of the primary users (PUs). Once find the spectrum idle, CR users start their transmission through it. Even while transmitting, they need to continue the sensing process so that they can leave the spectrum immediately whenever find a PU wanting to use the band. Therefore, detecting PUs is one of the main functions of cognitive radio before transmission and higher the detection probability ensures better protection to the primary users. However, it is not possible to attain a high detection probability (or a low miss detection probability) and low false alarm probability simultaneously as there is a tradeoff between false alarm probability ($P_{fa}$) and the probability of detection ($P_d$). In this paper, the author has provided a comprehensive study on different sensing techniques and discussed their advantages and disadvantages. Moreover, it is expected that, with this article, readers can have a through understanding of sensing techniques in CR and the current research trends in this area.

• The Transactions of The Korean Institute of Electrical Engineers
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• 제59권2호
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• pp.285-290
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• 2010

We investigate the outage probability in terms of QoS (quality of service) in indoor PLC network. We consider various kinds of appliances for realistic indoor PLC network. For estimation of the outage probability, we calculate the time-varying channel responses considering the loading conditions based on regular human activities and include the additive noise. We calculate the outage probability for each terminal and investigate relationship between the outage probability and the channel length, and transmit powers. Our results suggest that the outage probability is increased when the channel length becomes longer because more appliances affect the amount of reduced channel capacity and is not improved distinctly for very high and low outage threshold by increasing the transmit power. However, we can see outage probability improvement for 30% outage threshold case by increasing the transmit power.

• The Transactions of the Korean Institute of Electrical Engineers
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• 제45권2호
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• pp.325-328
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• 1996

In this paper, we proposed an estimation method of a posterior probability and PDF(Probability density function) using a feed forward neural network and code books of VQ(vector quantization). In this study, We estimates a posterior probability and probability density function, which compose a new parameter with well-known Mel cepstrum and verificate the performance for the five vowels taking from syllables by NN(neural network) and PNN(probabilistic neural network). In case of new parameter, showed the best result by probabilistic neural network and recognition rates are average 83.02%.

• Communications of the Korean Mathematical Society
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• 제37권3호
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• Journal of Educational Research in Mathematics
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• 제16권2호
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• pp.139-156
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• 2006

The concept of probability in current school mathematics has been dealt with in the classic viewpoint (mathematical probability) and part of the frequency viewpoint and axiomatic viewpoint have been introduced. However, since the exact understanding of the probability concepts is not possible only with the classic viewpoint, we need to research further on methods to complement classic viewpoint and emphasize various aspects of probability concepts (Lee, Kyung Hwa, 1996). Therefore, this study is to find out optimal computer simulation plans in teaching statistical probability. For the purpose, it examines how the nature of mathematical knowledge may be changed when statistical probability is taught with a use of computer simulation based on the Theory of Didactical Situation presented by Brousseau(1997). Next, it identifies how probability curriculum should be reconstituted for introducing statistical probability through computer simulation. Finally, it develops specific teaching materials that introduce statistical probability using computer simulation based on the results obtained.

• Journal for History of Mathematics
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• 제31권5호
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• pp.251-269
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• 2018

Empirical probability and classical probability, which are two interpretations of Kolmogorov's axiom, are two ways to recognize the chances of events occurring in the real world. In this paper, I analyzed and suggested the contents of the high school textbooks ${\ll}$Probability and Statistics${\gg}$, associated with two interpretations of probability and experiments on which two interpretations are based. By presenting the cases required expressly stating what the experiment is for supporting students' understanding of some concepts, it was discussed that stating or not stating what the experiment is should be carefully determined by the educational intent. Especially, I suggested that in the textbooks we contrast the good idea of calculating the ratios of two possibilities in the imaginary world of the classical probability with the normal idea of grasping the chances of events through the frequencies in the real world of the empirical probability, with distinguishing the experiments in two interpretations of probability. I also suggested that in the textbooks we make it clear that the Weak Law of Large Numbers justifies our expectations of the frequencies' reflecting the chances of events occurring in the real world under ideal conditions. Teaching and learning about the aesthetic elements and the practicality of imaginary mathematical thinking supported by these textbooks statements could be one form of Humanities education in mathematics as STEAM education.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• 제20권6호
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• pp.544-550
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• 2009

To analyze the threat decision performance of MWR(Missile Warning Radar) give analysis on condition that we decide the effective threat using the POC(Probability of Over Countermeasure)/PUC(Probability of Under Countermeasure). Thus, we execute the simulation using the Monte-Carlo method to analyze effect, but the execution time of simulation took longer than we expected. In this paper, the effect analysis is proposed using the probability model to reduce the execution time of simulation. We present the setting method of parameter for probability model and the effect analysis result of MWR using the simulation. Also, we present the comparison result of simulation execution time for Monte-Carlo and probability model.

• Journal of Environmental Science International
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• 제20권3호
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• pp.329-340
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• 2011

The probability concepts mainly used for rainfall or flood frequency analysis in water resources planning are the frequentist viewpoint that defines the probability as the limit of relative frequency, and the unknown parameters in probability model are considered as fixed constant numbers. Thus the probability is objective and the parameters have fixed values so that it is very difficult to specify probabilistically the uncertianty of these parameters. This study constructs the uncertainty evaluation model using Bayesian MCMC and Metropolis -Hastings algorithm for the uncertainty quantification of parameters of probability distribution in rainfall frequency analysis, and then from the application of Bayesian MCMC and Metropolis- Hastings algorithm, the statistical properties and uncertainty intervals of parameters of probability distribution can be quantified in the estimation of probability rainfall so that the basis for the framework configuration can be provided that can specify the uncertainty and risk in flood risk assessment and decision-making process.

• Journal of the Korea Institute of Information and Communication Engineering
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• 제15권1호
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• pp.57-62
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• 2011

This paper presents a study on the performance analysis on probability of bit error for wavelet in 4-ary SWSK system. The formula for the bit error probability in 4-ary SWSK system was derived from the conventional method. This paper experimentally implements the probability of bit error for Daubechies, Biorthogonal, Coiflet and Symlet wavelet using the conventional formula of bit error probability. Additionally, the performance of bit error probability is analyzed for the period and the number of wavelet taps. Based on the results, we confirmed that the performance of Coiflet and Symlet wavelet for the probability of bit error is superior to the other wavelet, and their probability of bit error are similar.