• Journal for History of Mathematics
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• v.31 no.5
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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.

• Journal of the Korea Society of Computer and Information
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• v.25 no.7
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• pp.175-182
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• 2020

Fisher's classical method for combining independent p-values from continuous distributions is widely used but it is known to be inadequate for combining p-values from discrete probability distributions. Instead, the discrete analog of Fisher's classical method is used as an alternative for combining p-values from discrete distributions. In this paper, firstly we obtain p-values from discrete probability distributions associated with multi-sample location test data (Fisher-Pitman test and Kruskall-Wallis test data) by permutation method, and secondly combine the permutaion p-values by the discrete analog of Fisher's classical method. And we finally compare the combined p-values from both the discrete analog of Fisher's classical method and Fisher's classical method.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.43-56
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• 2006

This paper aims to introduce a construction method for the 'Wooden Die for Drinking Game' and to find some geometrical structures and mathematics educational viewpoints. As the results, we get two methods which are eventually same with Figure 5 and Figure 6-3. We proved the ground that classical probability of this Die's each side showing up is one out of fourteen and introduced few other empirical probabilities with Table 1 to Table 3. Also, some Chinese characters were corrected and re-interpreted. In fact, 象人打鼻 changed to 衆人打鼻, and 醜物 is interpreted as 'ugly animal' such as frog, toad, earthworm or pine caterpillar.

• Journal for History of Mathematics
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• v.15 no.3
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• pp.65-74
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• 2002

In this paper we investigate an origin and development of the classical theory of probability. And we also investigate the law of large numbers and central limit theorem which are very important in tile probability theory.

• The Korean Journal of Applied Statistics
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• v.18 no.2
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• pp.445-452
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• 2005

We considered the frequency and classical probabilities under cuboctahedral die with 8 hexagons and 6 regular squares and compared with the frequency and logical probabilities under cuboctahedral die with 8 triangles and 6 regular squares.

• Korean Journal of Remote Sensing
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• v.2 no.1
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• pp.3-11
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• 1986

The current methods of estimating contest distribution function in contextual clarifier are to "classify and count", GTGM (ground-truth-guided-method) and unbiased estimator. In this paper we propose a new contextual classifier echoes context distribution is replaced by context probability that is estimated from transition probability. The classification accuracy increases considerably compared with the classical one.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• Journal of Communications and Networks
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• v.12 no.4
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• pp.366-374
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• 2010

Coded cooperation is a promising user cooperation scheme. In this paper, we first propose a novel network-coding-based coded cooperation scheme. When a user decodes its partner's information correctly in the first frame, it transmits the combination of the partner's parity bits and its own parity bits through network coding in the second frame. This is distinct from the classical scheme, where the user only transmits the partner's parity bits during cooperation. We analyze the outage probability of the proposed scheme, and show that it achieves a full diversity order. Numerical evaluations reveal that the proposed scheme outperforms the classical scheme when the inter-user channel is poor, yet is worse when the inter-user channel is strong. Also, the results show that the proposed scheme always outperforms that of no cooperation in various channel conditions while the performance of classical scheme is worse than that of no cooperation with the poor inter-user channels. This means that the performance of the proposed scheme is more stable than the classical scheme and the proposed scheme is more tolerant to the poor inter-user channels. To combine the advantages of the proposed scheme and the classical scheme under different inter-user channel conditions, we propose an adaptive solution. This adaptive scheme enhances the system performance considerably in all channel conditions in spite of the inter-user channel quality, at the expense of only one acknowledgement or non-acknowledgement bit.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.495-508
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• 2005

We investigated both classical and quantum properties of a damped harmonic oscillator with a time-variable elastic coefficient using invariant operator method. We acquired the energy eigenvalues, uncertainties and probability densities for several types of wave packet. The probability density corresponding to the displaced minimum wave packet expressed in terms of the time-dependent Gaussian function. The displaced minimum wave packet not only be attenuated but also oscillates about x = 0. We confirmed that there exist correspondence between quantum and classical behaviors for the time-dependent damped harmonic oscillator.

• Wind and Structures
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• v.1 no.4
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• pp.287-302
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• 1998

This paper formulates a probabilistic model which is able to represent the maximum instantaneous wind velocity. Unlike the classical methods, where the randomness is circumscribed within the mean maximum component, this model relies also on the randomness of the maximum value of the turbulent fluctuation. The application of the FOSM method furnishes the first and second statistical moments in closed form. The comparison between the results herein obtained and those supplied by classical methods points out the central role of the turbulence intensity. Its importance is exalted when extending the analysis from the wind velocity to the wind pressure.