Basic Concepts Of Probability Research Articles

Useful Measures of Exploration Performance

Summary Uncertainty about the outcomes of individual wells is a complicating factor in the development of performance measures for an exploration program. Using some basic concepts of probability and statistics to deal with this uncertainty, we have developed some tools to help exploration management compare results of an exploration program with expectations in a meaningful way. Introduction The collapse of oil and gas prices in the mid-1980's brought about a radically different investment climate for exploration. The industry had enjoyed a period when the oil and gas price scenarios that most people thought reasonable made almost any prospect look economically attractive. In that world, prospect economics seemed far less important than the explorationist's intuition about the prospect's desirability. Quantifying these beliefs and using historical data to substantiate them seemed unnecessary. After the fall in prices, most managements revised their future price scenarios and found that many of their exploratory plays were uneconomic or marginal. Exploration budgets were cut. We began to look more closely at the economics of individual plays or prospects before drilling. Explorationists' beliefs came under closer scrutiny, and at Arco we felt an urgency to measure how well we were doing with our exploration program, which used a substantial share of limited capital resources. program, which used a substantial share of limited capital resources. Measuring the results or performance of an exploration effort in ways that enhance future decision-making capability is difficult. In this paper, we focus on a few aspects of performance measurement that we believe paper, we focus on a few aspects of performance measurement that we believe have crucial implications for intelligent decision-making in exploration. Here we focus on the estates of key parameters made by the explorationists before a prospect is drilled. We believe that, by far, the two most important parameters are the probability of finding hydrocarbons (the "chance factor") and the reserves discovered if the well is successful. Explorationists have historical data, geologic models, and their own experience as aids, but the estimates they make of these key parameters are largely subjective, resulting from an informed judgment about what is reasonable. The uncertainty inherent in exploration further complicates the measurement of performance. We need to allow for this uncertainty when we compare actual outcomes with our predrilling estimates of key parameters. Most of us do not reject the idea that the probability of heads on the flip of a coin is one-half, even if we flip twice and get two tails in a row. Likewise, it doesn't make much sense to condemn the explorationist who had estimated the probability of success on each of two wells at 50% when both turn out to be dry. We need to use and understand some probability concepts to compare actual and estimated results properly. But probability concepts to compare actual and estimated results properly. But before we look at methodology, let us test our intuition in a hypothetical situation. Intuition and Exploration Results Let us assume that our exploration department has drilled 20 exploratory wells in the first 6 months of this year. To keep things simple, let us assume that the explorationists assigned a probability of success (chance factor) of 20% to each of these wells. Also in the interest of simplicity, let us assume that their estimate of the reserves (given a success) on each well was identical and equal to 10 million bbl. It is easy to calculate the chance-weighted value or "expected value" of reserves for each well as 2 million bbl. (We discuss the concept of expected value in the next section). Because we have drilled 20 of these identical wells, we can multiply the expected reserves on each well by 20 and calculate the expected reserves for the total program as 40 million bbl. Let us assume that we actually discovered 24 million bbl alter drilling 20 wells. Thus, our actual reserves discovered are 40% less than the expected amount. This, of course, is cause for concern. But is the result strong evidence that the estimates of our explorationists were biased to the high side, or could the actual outcome reasonably be ascribed to chance (bad luck)? Is it time to overhaul our whole estimating process? Intuition might suggest that it is, but we need to delve into the world of probability to gain the understanding needed to answer these questions properly. properly. Reserve and Chance Probability Assessment Probability Assessment One thing we can be sure of in any exploration program is that outcomes will never be exactly as predicted.

The cognitive effects of a mathematics in-service workshop on elementary school teachers

Siegler's rule assessment methodology was used to investigate the cognitive effects of a 32 hour mathematics in-service workshop on 28 elementary shool teachers. This paper reports on attempts (a) to assess the levels of cognitive understanding of the basic concepts of proportion, probability, and correlation among elementary teachers, and (b) to change teachers' levels in understanding these concepts by a method of “direct instruction”. Significant improvements were noted in the levels of cognitive development associated with the concept of proportion. Though nonsignificant improvements were noted in the concepts of probability and correlation, all the teachers were assigned to the highest cognitive rule associated with the probability concept at the end of the workshop.

Statistical Methods for the Analysis of Biomedical Data

Dedication.Preface to the 1987 Edition. Preface to the 2002 Edition. Acknowledgments. 1. Introduction. 2. Descriptive Statistics. 3. Basic Probability Concepts. 4. Further Aspects of Probability. 5. Confidence Intervals and Hypothesis Testing: General Considerations and Applications. 6. Comparison of Two Groups: t Tests and Rank Tests. 7. Comparison of Two Groups: Chi Square and Related Procedures. 8. Tests of Independence and Measures of Association for Two Random Variables. 9. Least Square Regression Methods: Predicting One Variable from Another. 10. Comparing More Than Two Groups of Observations: Analysis of Variance for Comparing Groups. 11. Comparing More Than Two Groups of Observations: Rank Analysis of Variance for Group Comparisons. 12. Comparing More than Two Groups of Observations: Chi Square and Related Procedures. 13. Special Topics in Analysis of Epidemiologic and Clinical Data: Studying Association between a Disease and a Characteristic. 14. Estimation and Comparison of Survival Curves. 15. Multiple Linear Regression Methods: Predicting One Variable from Two or More Other Variables. Appendix.Topic Index.

Introductory Management Science

(NOTE: At the End of Each Chapter is a Video Case.) 1. Introduction: Models and Modeling. I: DETERMINISTIC MODELS. 2. Linear Programming: Formal and Spreadsheet Models. 3. Linear Programming: Geometric Representations and Graphical Solutions. 4. Analysis of LP Models: The Graphical Approach. 5. Linear Programs: Computer Analysis, Interpreting Sensitivity Output, and the Dual Problem. 6. Linear Programming: The Simplex Method. 7. Linear Programming: Special Applications. 8. Integer and Quadratic Programming. 9. Network Models. 10. Inventory Control with Known Demand. 11. Heuristics, Multiple Objectives, and Goal Programming. 12. Calculus-Based Optimization and an Introduction to Nonlinear Programming. II: PROBABILISTIC MODELS. 13. Simulation. 14. Decision Theory and Decision Trees. 15. Project Management: PERT and CPM. 16. Inventory Models with Probabilistic Demand. 17. Queuing Models. 18. Forecasting. Answers to Odd-Numbered Problems. Appendix A: Basic Concepts in Probability. Using LINDO. Index.

Quality Programming: Developing and Testing Software with Statistical Quality Control

Introduction. Basic Concepts in Probability. Important Statistical Distributions for Software Quality Control. Random Number Generation. Sampling Techniques and Statistical Inference. Acceptance Sampling. Modeling. Requirements Specification. Concurrent Software Design and Test Design. Concurrent Implementation of Software Design and Test Design. Software Testing, Integration, Verification, Validation, and Debugging. Software Acceptance. Quality Programming: A Case Study. Software Reliability. Software Quality and Productivity: What Top Management Must Do. Appendixes. Index.

Probability and the Seating Chart

The problem-solving activities outlined here add to the collection of applications- at the middle school level and above- dealing with basic probability concepts. The context is an unusual and unexpected one: the classroom seating chart. Students need to know these concepts because they are at the heart of decision-making processes. Solving problems of the type that follow reinforces these concepts and gives students practice in the problem-solving techniques of counting, finding patterns, using diagrams, and generalizing.

A Look at Frequency Distributions for Sports Scores

Frequency distributions are familiar to almost all sports fans. Most common are one-way distributions in which the frequency of occurrence for each of the related categories is given. Table 1 gives an example of such a distribution. Several basic concepts in statistics and probability can be illustrated here. For example, the mean, median, mode, range, standard deviation, and other sample statistics can be calculated, as well as the a posteriori probability that a certain score occurs (table 2).

Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research

There is a growing movement to introduce elements of statistics and probability into the secondary and even the elementary school curriculum, as part of basic literacy in mathematics. Although many articles in the education literature recommend how to teach statistics better, there is little published research on how students actually learn statistics concepts. The experience of psychologists, educators, and statisticians alike is that a large proportion of students, even in college, do not understand many of the basic statistical concepts they have studied. Inadequacies in prerequisite mathematics skills and abstract reasoning are part of the problem. In addition, research in cognitive science demonstrates the prevalence of some intuitive ways of thinking that interfere with the learning of correct statistical reasoning. The literature reviewed in this paper indicates a need for collaborative, cross-disciplinary research on how students come to think correctly about probability and statistics.

Difficulties in Learning Basic Concepts in Probability and Statistics: Implications for Research

There is a growing movement to introduce elements of statistics and probability into the secondary and even the elementary school curriculum, as part of basic literacy in mathematics. Although many articles in the education literature recommend how to teach statistics better, there is little published research on how students actually learn statistics concepts. The experience of psychologists, educators, and statisticians alike is that a large proportion of students, even in college, do not understand many of the basic statistical concepts they have studied.

Statistical Methods for the Analysis of Biomedical Data.

Dedication.Preface to the 1987 Edition. Preface to the 2002 Edition. Acknowledgments. 1. Introduction. 2. Descriptive Statistics. 3. Basic Probability Concepts. 4. Further Aspects of Probability. 5. Confidence Intervals and Hypothesis Testing: General Considerations and Applications. 6. Comparison of Two Groups: t Tests and Rank Tests. 7. Comparison of Two Groups: Chi Square and Related Procedures. 8. Tests of Independence and Measures of Association for Two Random Variables. 9. Least Square Regression Methods: Predicting One Variable from Another. 10. Comparing More Than Two Groups of Observations: Analysis of Variance for Comparing Groups. 11. Comparing More Than Two Groups of Observations: Rank Analysis of Variance for Group Comparisons. 12. Comparing More than Two Groups of Observations: Chi Square and Related Procedures. 13. Special Topics in Analysis of Epidemiologic and Clinical Data: Studying Association between a Disease and a Characteristic. 14. Estimation and Comparison of Survival Curves. 15. Multiple Linear Regression Methods: Predicting One Variable from Two or More Other Variables. Appendix.Topic Index.

A mathematical model for headway variance of fixed-route buses

A mathematical model for computing and analysing headway variance of fixed-route buses offering scheduled service is developed. The model assumes a situation where both the passengers' OD pattern and the bus-route structure do not have any particular form but the number of passengers served at any bus station is a stationary Poisson process. Basic probability concepts are mostly used in deriving the model. Innovations in the model are the inclusion of a skip probability at a stop and the correlation factors between successive bus loads at a loading point and between the travel times of successive buses on a link. The model is, therefore, applicable to a wider range of situations than was possible with the earlier models. Results indicate that bus loading conditions and traffic conditions along the route are the major factors responsible for headway variability. The developed model can be used to determine the relative importance of these factors on headway variance at individual stopping station and thereby simplify the task of evolving effective countermeasures in any given situation. A numerical example that illustrates the application of the model is also given.

Rote versus Conceptual Emphases in Teaching Elementary Probability

Forty-eight students with no previous exposure to probability or statistics read one of three texts that varied in the emphasis placed on rote and conceptual learning of basic concepts of elementary probability. A qualitative analysis of errors on a postinstruction test employed a model of problem solving whose stages were categorization of the problem, retrieval of the appropriate formula, and translation of values from the problem into the formula. Variations in performance on problems requiring the same formula for solution were largely attributable to surface features that affected the ease of categorization and translation. Students who read a text that emphasized conceptual learning tended to be less sensitive to surface features, which parallels results regarding novices and experts in various content domains.

Probability, exchangeability and extremes: with discussion of iceberg loading

Abstract The basic concepts of probability and utility, as well as their interrelationship, are reviewed. The duality embodied in the definitions of these quantities is emphasized. The assumptions of exchangeability as an alternative to independence, in assessing the implications of data sets and in problems of inference, is shown to offer the opportunity for considerable improvement in statistical analysis. Exchangeability implies that the order of a sequence of random events or quantities is not of significance. The use of a basic urn model in formulating problems involving exchangeability is demonstrated. The extension of the analysis to continuous random quantities as well as to problems of extremes is summarized. An example of the analysis of arrival of icebergs at discrete points in time at the location of an offshore structure is included and it is shown that the results include the uncertainty resulting from short data bases. The added risk associated with this uncertainty is acknowledged implicit...

Fuzzy decision trees

We propose here to extend the decision trees method to the case when the involved data (probabilities, cost, profits, losses) appear as words belonging to the common language whose semantic representations are fuzzy sets. First we discuss the reasons why such an extension is to be aimed at. Then in the fuzzy case we carry out a reformalization of the basic concepts of probability and utility theory. Finally we show how these reformalized concepts can be applied to fuzzy decision trees.

Numerical Solution of Highly Non-Linear Problems

"Numerical Solution of Highly Non-Linear Problems." Journal of the Operational Research Society, 31(10), p. 958

Basic Concepts of Probability— What Do People Know?*

Basic Concepts of Probability— What Do People Know?*

Basic Concepts of Probability and Statistics

Basic Concepts of Probability and Statistics

Basic Concepts of Probability and Statistics. By J. L. Hodges and E. L. Lehmann. Pp. xiii, 375. £2.80. 1964. (Holden-Day.)

Basic Concepts of Probability and Statistics. By J. L. Hodges and E. L. Lehmann. Pp. xiii, 375. £2.80. 1964. (Holden-Day.)

Basic Concepts of Probability and Statistics.

Preface Part I. Probability: 1. Probability models 2. Sampling 3. Product models 4. Conditional probability 5. Random variables 6. Special distributions 7. Multivariate distributions Part II. Statistics. Introduction to Statistics: 8. Estimation 9. Estimation in measurement and sampling models 10. Optimum methods of estimation 11. Tests of significance 12. Tests for comparative experiments 13. Concept of power Tables Selected answers to problems Index Example index.

Basic Concepts of Probability and Statistics, Second Edition.

Basic Concepts of Probability and Statistics, Second Edition.