• Title/Summary/Keyword: probability

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Probabilistic Forecasting of Seasonal Inflow to Reservoir (계절별 저수지 유입량의 확률예측)

  • Kang, Jaewon
    • Journal of Environmental Science International
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    • v.22 no.8
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    • pp.965-977
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    • 2013
  • Reliable long-term streamflow forecasting is invaluable for water resource planning and management which allocates water supply according to the demand of water users. It is necessary to get probabilistic forecasts to establish risk-based reservoir operation policies. Probabilistic forecasts may be useful for the users who assess and manage risks according to decision-making responding forecasting results. Probabilistic forecasting of seasonal inflow to Andong dam is performed and assessed using selected predictors from sea surface temperature and 500 hPa geopotential height data. Categorical probability forecast by Piechota's method and logistic regression analysis, and probability forecast by conditional probability density function are used to forecast seasonal inflow. Kernel density function is used in categorical probability forecast by Piechota's method and probability forecast by conditional probability density function. The results of categorical probability forecasts are assessed by Brier skill score. The assessment reveals that the categorical probability forecasts are better than the reference forecasts. The results of forecasts using conditional probability density function are assessed by qualitative approach and transformed categorical probability forecasts. The assessment of the forecasts which are transformed to categorical probability forecasts shows that the results of the forecasts by conditional probability density function are much better than those of the forecasts by Piechota's method and logistic regression analysis except for winter season data.

An Investigation on the Effect of Utility Variance on Choice Probability without Assumptions on the Specific Forms of Probability Distributions (특정한 확률분포를 가정하지 않는 경우에 효용의 분산이 제품선택확률에 미치는 영향에 대한 연구)

  • Won, Jee-Sung
    • Korean Management Science Review
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    • v.28 no.1
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    • pp.159-167
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    • 2011
  • The theory of random utility maximization (RUM) defines the probability of an alternative being chosen as the probability of its utility being perceived as higher than those of all the other competing alternatives in the choice set (Marschak 1960). According to this theory, consumers perceive the utility of an alternative not as a constant but as a probability distribution. Over the last two decades, there have been an increasing number of studies on the effect of utility variance on choice probability. The common result of the previous studies is that as the utility variance increases, the effect of the mean value of the utility (the deterministic component of the utility) on choice probability is reduced. This study provides a theoretical investigation on the effect of utility variance on choice probability without any assumptions on the specific forms of probability distributions. This study suggests that without assumptions of the probability distribution functions, firms cannot apply the marketing strategy of maximizing choice probability (or market share), but can only adopt the strategy of maximizing the minimum or maximum value of the expected choice probability. This study applies the Chebyshef inequality and shows how the changes in utility variances affect the maximum of minimum of choice probabilities and provides managerial implications.

3rd, 4th and 5th Graders' Probability Understanding (초등학교 3, 4, 5학년 학생들의 확률 이해 실태)

  • Yoon, Hye-Young;Lee, Kwang-Ho
    • Education of Primary School Mathematics
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    • v.14 no.1
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    • pp.69-79
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    • 2011
  • The purpose of this study is to analyze 3rd, 4th and 5th graders' probability understanding and raise issues concerning instructional methods and search for the possibility of learning probability. For the purpose, a descriptive study through pencil-and-paper test regarding fairness, sample space, probability of event, probability comparison, independence and conditional probability was conducted. The following conclusions were drawn from the results obtained in this study. First, the 3rd, 4th, and 5th grade students scored the highest in the sample space questions. In descending order of skill, the students scored the highest in sample space following probability of events, fairness and probability comparison. Second, however, the level of independence understanding was low. There was no meaningful differences between grades and the conditional probability was the least understood. The independence is difficult to develop naturally according to cognitive development. The conditional probability recognizing the probability of an event changes in non-replacement situations was very difficult for these students. Third, there were significant differences between the 5th graders and the 3rd and 4th graders in the probability comparison questions. It shows that 5th graders understand the concept of proportion when they compare equal ratio probability of an event. The 3rd graers could do different ratio probability of an event more easily than equal ratio probability of an event after they were instructed on probability comparison.

Calculation of Life-Time Death Probability due Malignant Tumors Based on a Sampling Survey Area in China

  • Yuan, Ping;Chen, Tie-Hui;Chen, Zhong-Wu;Lin, Xiu-Quan
    • Asian Pacific Journal of Cancer Prevention
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    • v.15 no.10
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    • pp.4307-4309
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    • 2014
  • Purpose: To calculate the probability of one person's life-time death caused by a malignant tumor and provide theoretical basis for cancer prevention. Materials and Methods: The probability of one person's death caused by a tumor was calculated by a probability additive formula and based on an abridged life table. All data for age-specific mortality were from the third retrospective investigation of death cause in China. Results: The probability of one person's death caused by malignant tumor was 18.7% calculated by the probability additive formula. On the same way, the life-time death probability caused by lung cancer, gastric cancer, liver cancer, esophageal cancer, colorectal and anal cancer were 4.47%, 3.62%, 3.25%, 2.25%, 1.11%, respectively. Conclusions: Malignant tumor is still the main cause of death in one's life time and the most common causes of cancer death were lung, gastric, liver, esophageal, colorectal and anal cancers. Targeted forms of cancer prevention and treatment strategies should be worked out to improve people's health and prolong life in China. The probability additive formula is a more scientific and objective method to calculate the probability of one person's life-time death than cumulative death probability.

A Didactic Analysis of Conditional Probability (조건부확률 개념의 교수학적 분석과 이해 분석)

  • Lee, Jung-Yeon;Woo, Jeong-Ho
    • Journal of Educational Research in Mathematics
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    • v.19 no.2
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    • pp.233-256
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    • 2009
  • The notions of conditional probability and independence are fundamental to all aspects of probabilistic reasoning. Several previous studies identified some misconceptions in students' thinking in conditional probability. However, they have not analyzed enough the nature of conditional probability. The purpose of this study was to analyze conditional probability and students' knowledge on conditional probability. First, we analyzed the conditional probability from mathematical, historico-genetic, psychological, epistemological points of view, and identified the essential aspects of the conditional probability. Second, we investigated the high school students' and undergraduate students' thinking m conditional probability and independence. The results showed that the students have some misconceptions and difficulties to solve some tasks with regard to conditional probability. Based on these analysis, the characteristics of reasoning about conditional probability are investigated and some suggestions are elicited.

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A comparative analysis of the 2009-revised curriculum and 2015-revised curriculum on the definition and introduction of continuous probability distribution (연속확률분포의 정의와 도입 방법에 대한 2009개정 교육과정과 2015개정 교육과정의 비교 분석 연구)

  • Heo, Nam Gu
    • The Mathematical Education
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    • v.58 no.4
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    • pp.531-543
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    • 2019
  • Continuous probability distribution was one of the mathematics concept that students had difficulty. This study analyzed the definition and introduction of the continuous probability distribution under the 2009-revised curriculum and 2015-revised curriculum. In this study, the following subjects were studied. Firstly, definitions of continuous probability variable in 'Probability and Statistics' textbook developed under the 2009-revised curriculum and 2015-revised curriculum were analyzed. Secondly, introductions of continuous probability distribution in 'Probability and Statistics' textbook developed under the 2009-revised curriculum and 2015-revised curriculum were analyzed. The results of this study were as follows. First, 8 textbooks under the 2009-revised curriculum defined the continuous probability variable as probability variable with all the real values within a range or an interval. And 1 textbook under the 2009-revised curriculum defined the continuous probability variable as probability variable when the set of its value is uncountable. But all textbooks under the 2015-revised curriculum defined the continuous probability variable as probability variable with all the real values within a range. Second, 4 textbooks under the 2009-revised curriculum and 4 textbooks under 2015-revised curriculum introduced a continuous random distribution using an uniformly distribution. And 5 textbooks under the 2009-revised curriculum and 5 textbooks under the 2015-revised curriculum introduced a continuous random distribution using a relative frequency density.

NORMAL FUZZY PROBABILITY FOR TRAPEZOIDAL FUZZY SETS

  • Kim, Changil;Yun, Yong Sik
    • East Asian mathematical journal
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    • v.29 no.3
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    • pp.269-278
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    • 2013
  • A fuzzy set A defined on a probability space (${\Omega}$, $\mathfrak{F}$, P) is called a fuzzy event. Zadeh defines the probability of the fuzzy event A using the probability P. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. We calculate the normal fuzzy probability for generalized trapezoidal fuzzy sets and give some examples.

Efficient Channel State Feedback Scheme for Opportunistic Scheduling in OFDMA Systems by Scheduling Probability Prediction

  • Ko, Soomin;Lee, Jungsu;Lee, Byeong Gi;Park, Daeyoung
    • Journal of Communications and Networks
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    • v.15 no.6
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    • pp.589-600
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    • 2013
  • In this paper, we propose a new feedback scheme called mode selection-based feedback by scheduling probability prediction (SPP-MF) for channel state feedback in OFDMA downlink system. We design the scheme such that it determines the more desirable feedback mode among selective feedback by scheduling probability prediction (SPP-SF) mode and bitmap feedback by scheduling probability prediction (SPP-BF) mode, by calculating and comparing the throughputs of the two modes. In both feedback modes, each user first calculates the scheduling probability of each subchannel (i.e., the probability that a user wins the scheduling competition for a subchannel) and then forms a feedback message based on the scheduling probability. Specifically, in the SPP-SF mode, each user reports the modulation and coding scheme (MCS) levels and indices of its best S subchannels in terms of the scheduling probability. In the SPP-BF mode, each user determines its scheduling probability threshold. Then, it forms a bitmap for the subchannels according to the scheduling probability threshold and sends the bitmap along with the threshold. Numerical results reveal that the proposed SPP-MF scheme achieves significant performance gain over the existing feedback schemes.

An Analysis of the 8th Grade Probability Curriculum in Accordance with the Distribution Concepts (분포 개념의 연계성 목표 관점에 따른 중학교 확률 단원 분석)

  • Lee, Young-Ha;Huh, Ji-Young
    • Journal of Educational Research in Mathematics
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    • v.20 no.2
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    • pp.163-183
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    • 2010
  • It has long been of controversy what the meanings of probability is. And a century has past after the mathematical probability has been at the center of the school curriculum of it. Recently statistical meaning of probability becomes important for various reasons. However the simple modification of its definition is not enough. The computational reasoning of the probability and its practical application needs didactical changes and new instructional transformations along with the modification of it. Most of the current text books introduce probability as a limit of the relative frequencies, a statistical probability. But when the probability computation of the union of two events, or of the simultaneous events is faced on, they use mathematical probability for explanation and practices. Accordingly there is a gap for students in understanding those. Probability is an intuitive concept as far as it belongs to the domain of the experiential frequency. And frequency distribution must be the instructional bases for the (statistical) probability novices. This is what we mean by the probability in accordance with the distribution concepts. First of all, in order to explain the probability of the complementary event we should explain the empirical relative frequency of it first. These are the case for the union of two events and for the simultaneous events. Moreover we need to provide a logic of probabilistic guesses, inferences and decision, which we introduce with the name “the likelihood principle”, the most famous statistical principle. We emphasized this be done through the problems of practical decision making.

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A Study on Conditional Probability (조건부확률에 관한 연구)

  • Cho, Cha-Mi
    • Journal of Educational Research in Mathematics
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    • v.20 no.1
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    • pp.1-20
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    • 2010
  • Conditional probability may look simple but it raises various misconceptions. Preceding studies are mostly about such misconceptions. However, instead of focusing on those misconceptions, this paper focused on what the mathematical essence of conditional probability which can be applied to various situations and how good teachers' understanding on that is. In view of this purpose, this paper classified conditional probability which have different ways of defining into two-relative conditional probability which can be get by relative ratio and if-conditional probability which can be get by the inference of the situation change of conditional event. Yet, this is just a superficial classification of resolving ways of conditional probability. The purpose of this paper is in finding the mathematical essence implied in those, and by doing that, tried to find out how well teachers understand about conditional probability which is one integrated concept.

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