The document is a lecture presentation on statistics that includes:
1. An outline of chapter contents which covers probability, random variables, statistical intervals, and hypothesis testing.
2. Learning objectives that cover understanding sample spaces, calculating probabilities, counting techniques, and conditional probabilities.
3. Examples that illustrate sample spaces, events, permutations, combinations, and probability rules.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
A simple unstructured finite volume scheme is used to solve the two-dimensional
shallow water equations (SWEs) for simulation of dam break flows over irregular beds
involving wet and dry interfaces. In space, we construct a balancing higher order upwind
scheme on unstructured triangular mesh to approximate the convective and source term
due to bed slop. We improve the scheme to treat the cases of flow over dry beds. For
temporal derivative approximation, a second-order explicit Runge-Kutta is used. We
apply the scheme for several theoretical two-dimensional numerical experiments
involving dam-break flows with moving wet-dry fronts over irregular bed topography.
Promising results are obtained.
1) The document presents regression results from Chapter 7 of the textbook "Basic Econometrics" by Gujarati and Porter. It discusses multiple regression analysis and the problem of estimation.
2) Various regression models are estimated using different variables and datasets. The results, standard errors, and other regression outputs like R-squared are reported for each model.
3) Key concepts discussed include omitted variable bias, partial regression coefficients, elasticities, and the consequences of model misspecification.
The Odd Generalized Exponential Log Logistic Distributioninventionjournals
We propose a new lifetime model, called the odd generalized exponential log logistic distribution (OGELLD).We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The maximum likelihood method is used for estimating the model parameters and the Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real lifetime data.
Modeling of manufacturing of a field effect transistor to determine condition...ijcsa
In this paper we introduce an approach to model technological process of manufacture of a field-effect
heterotransistor. The modeling gives us possibility to optimize the technological process to decrease length
of channel by using mechanical stress. As accompanying results of the decreasing one can find decreasing
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
Control Synthesis of Electro Hydraulic Drive Based on the Concept of Inverse ...ijtsrd
Electro hydraulic drives are widely used in various branches of technology due to a number of its advantages, which include significant specific power the ratio of power developed by the drive to its mass , high speed and the ability to position the output link with a sufficient degree of accuracy. However, hydraulic drives are non linear objects, which makes it difficult to synthesize drive control, which provides the required dynamic characteristics. This paper presents an approach to solving the problem of constructing a control algorithm based on the concept of inverse problems of dynamics by an electro hydraulic drive, consisting structurally of an electro hydraulic amplifier and an executive hydraulic cylinder. Soe Nay Lynn Aung | Akimenko D. A "Control Synthesis of Electro-Hydraulic Drive Based on the Concept of Inverse Dynamics Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27823.pdf Paper URL: https://www.ijtsrd.com/engineering/other/27823/control-synthesis-of-electro-hydraulic-drive-based-on-the-concept-of-inverse-dynamics-problems/soe-nay-lynn-aung
Numerical simulation of marangoni driven boundary layer flow over a flat plat...eSAT Journals
Abstract
A numerical algorithm is presented for studying Marangoni convection flow over a flat plate with an imposed temperature
distribution. Plate temperature varies with x in the following prescribed manner: where A and k are constants.
By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of
nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton
Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab
environment. Velocity profiles for various values of k, and temperature profiles for various Prandtl number and k are illustrated
graphically. The results of the present simulation are then compared with the previous works available in literature with good
agreement.
Keywords: Matlab, Marangoni Convection, Numerical Simulation, Surface Tension, Flat Plate.
Numerical study of natural convection in an enclosed square cavity using cons...eSAT Journals
This document summarizes a numerical study of natural convection in an enclosed square cavity using the Constrained Interpolated Profile (CIP) method. The CIP method was used to simulate the natural convection heat transfer and fluid flow in a square cavity with differentially heated side walls. The streamlines and isotherms obtained for Rayleigh numbers of 103, 104, and 105 were compared to published literature and found to be in good agreement. The CIP method solves the advection phase equation using CIP and the non-advection phase using finite difference methods. Governing equations for the vorticity transport and energy equations are presented and discretized for solution using the CIPNSE method.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
A simple unstructured finite volume scheme is used to solve the two-dimensional
shallow water equations (SWEs) for simulation of dam break flows over irregular beds
involving wet and dry interfaces. In space, we construct a balancing higher order upwind
scheme on unstructured triangular mesh to approximate the convective and source term
due to bed slop. We improve the scheme to treat the cases of flow over dry beds. For
temporal derivative approximation, a second-order explicit Runge-Kutta is used. We
apply the scheme for several theoretical two-dimensional numerical experiments
involving dam-break flows with moving wet-dry fronts over irregular bed topography.
Promising results are obtained.
1) The document presents regression results from Chapter 7 of the textbook "Basic Econometrics" by Gujarati and Porter. It discusses multiple regression analysis and the problem of estimation.
2) Various regression models are estimated using different variables and datasets. The results, standard errors, and other regression outputs like R-squared are reported for each model.
3) Key concepts discussed include omitted variable bias, partial regression coefficients, elasticities, and the consequences of model misspecification.
The Odd Generalized Exponential Log Logistic Distributioninventionjournals
We propose a new lifetime model, called the odd generalized exponential log logistic distribution (OGELLD).We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The maximum likelihood method is used for estimating the model parameters and the Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real lifetime data.
Modeling of manufacturing of a field effect transistor to determine condition...ijcsa
In this paper we introduce an approach to model technological process of manufacture of a field-effect
heterotransistor. The modeling gives us possibility to optimize the technological process to decrease length
of channel by using mechanical stress. As accompanying results of the decreasing one can find decreasing
of thickness of the heterotransistors and increasing of their density, which were comprised in integrated
circuits.
Control Synthesis of Electro Hydraulic Drive Based on the Concept of Inverse ...ijtsrd
Electro hydraulic drives are widely used in various branches of technology due to a number of its advantages, which include significant specific power the ratio of power developed by the drive to its mass , high speed and the ability to position the output link with a sufficient degree of accuracy. However, hydraulic drives are non linear objects, which makes it difficult to synthesize drive control, which provides the required dynamic characteristics. This paper presents an approach to solving the problem of constructing a control algorithm based on the concept of inverse problems of dynamics by an electro hydraulic drive, consisting structurally of an electro hydraulic amplifier and an executive hydraulic cylinder. Soe Nay Lynn Aung | Akimenko D. A "Control Synthesis of Electro-Hydraulic Drive Based on the Concept of Inverse Dynamics Problems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27823.pdf Paper URL: https://www.ijtsrd.com/engineering/other/27823/control-synthesis-of-electro-hydraulic-drive-based-on-the-concept-of-inverse-dynamics-problems/soe-nay-lynn-aung
Numerical simulation of marangoni driven boundary layer flow over a flat plat...eSAT Journals
Abstract
A numerical algorithm is presented for studying Marangoni convection flow over a flat plate with an imposed temperature
distribution. Plate temperature varies with x in the following prescribed manner: where A and k are constants.
By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a pair of
nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton
Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab
environment. Velocity profiles for various values of k, and temperature profiles for various Prandtl number and k are illustrated
graphically. The results of the present simulation are then compared with the previous works available in literature with good
agreement.
Keywords: Matlab, Marangoni Convection, Numerical Simulation, Surface Tension, Flat Plate.
Numerical study of natural convection in an enclosed square cavity using cons...eSAT Journals
This document summarizes a numerical study of natural convection in an enclosed square cavity using the Constrained Interpolated Profile (CIP) method. The CIP method was used to simulate the natural convection heat transfer and fluid flow in a square cavity with differentially heated side walls. The streamlines and isotherms obtained for Rayleigh numbers of 103, 104, and 105 were compared to published literature and found to be in good agreement. The CIP method solves the advection phase equation using CIP and the non-advection phase using finite difference methods. Governing equations for the vorticity transport and energy equations are presented and discretized for solution using the CIPNSE method.
A comparative study of three validities computation methods for multimodel ap...IJECEIAES
The multimodel approach offers a very satisfactory results in modelling, diagnose and control of complex systems. In the modelling case, this approach passes by three steps: the determination of the model’s library, the validities computation and the establishment of the final model. In this context, this paper focuses on the elaboration of a comparative study between three recent methods of validities computation. Thus, it highlight the method that offers the best performances in term of precision. To achieve this goal, we apply, these three methods on two simulation examples in order to compare their performances.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam
The only way I could do that was if you had to do a lot more work and then you would be done by yourself so you would be fine and then I could just go home to you if I needed you and you could just come over here or I can just go home if I need
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document outlines a group project on derivatives. It includes definitions of derivatives, a brief history of their development, and examples of applications in various fields such as automobiles, business, and mathematics. Rules for finding derivatives of sums, quotients, logarithmic, trigonometric, and exponential functions are also presented, along with examples of applying the rules to calculate derivatives.
The document discusses building human-based software estimation models that are accurate, intuitive, and easy to understand. It presents an approach using correlation and scale factors between estimated and actual effort. Experiments on a dataset of 178 samples show that combining correlation and scale factors into a decision tree achieves up to 93.3% accuracy. The resulting model bridges expert and algorithmic estimation methods.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
The document describes an experiment on flow system control using a PID controller. The objectives are to obtain the system characteristics like overshoot, rise time, settling time, period, and transport delay. It introduces PID controllers and how they work in a closed loop system using proportional, integral, and derivative modes. The apparatus section outlines the experimental setup, which uses a flow system with a square wave input and adjustable setpoint and proportional gain. Calculations are shown for analyzing the system response based on these parameters.
This document presents a multi-objective optimization model for integrated production and distribution scheduling. The objectives are to minimize total weighted tardiness and total distribution costs. A mixed integer programming formulation is developed with constraints for job precedence, vehicle capacity, and delivery times. A genetic algorithm using NSGA-II is proposed as a solution methodology, with chromosome representation, crossover, mutation and crowding distance calculation described. An example problem is presented to illustrate the model and solution approach.
Subject Title: Engineering Numerical Analysis
Subject Code: ID-302
Contents of this chapter:
Mathematical preliminaries,
Solution of equations in one variable,
Interpolation and polynomial Approximation,
Numerical differentiation and integration,
Initial value problems for ordinary differential equations,
Direct methods for solving linear systems,
Iterative techniques in Matrix algebra,
Solution of non-linear equations.
Approximation theory;
Eigen values and vector;
Modeling and implementation of a proportional derivative controller for elect...Alexander Decker
This document summarizes a research article that models and implements a proportional-derivative (P-D) controller for an electroviscous damper. The researchers developed a mathematical model of the damper system and used MATLAB to simulate the open-loop and closed-loop step responses. The results showed that the P-D controller reduced overshoot and settling time compared to just proportional control, with little effect on rise time and steady-state error. The controller successfully controlled the performance of the electroviscous damper.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
COMPARATIVE ANALYSIS OF CONVENTIONAL PID CONTROLLER AND FUZZY CONTROLLER WIT...IJITCA Journal
All the real systems exhibits non-linear nature,conventional controllers are not always able to provide good and accurate results. Fuzzy Logic Control is used to obtain better response. A model for simulation is designed and all the assumptions are made before the development of the model. An attempt has been made to analyze the efficiency of a fuzzy controller over a conventional PID controller for a three tank level control system using fuzzification & defuzzification methods and their responses are compared. Analysis is done through computer simulation using Matlab/Simulink toolbox. This study shows that the application of Fuzzy Logic Controller (FLC) gives the best response with triangular membership function and centroid defuzzification method.
This document presents a multi-objective optimization method for economic emission load dispatch (EELD) that considers economy, emissions, and transmission line security as objectives. The problem is formulated to minimize total fuel costs and emissions while maximizing line security for a power system. The multi-objective problem is converted to a single objective using goal attainment and then solved using simulated annealing. Results are presented for a 30-bus and 57-bus IEEE test case system to demonstrate the proposed method.
This document discusses evaluating reliability parameters for a power plant using algebra of logics. The power plant has two identical generators in standby redundancy to power four machines that can operate in pairs. The author develops a mathematical model representing the system configuration and operating conditions using Boolean logic. Equations are formulated to represent the conditions for successful operation of the power plant. The model is then solved using orthogonalization algorithms and algebra of logics to obtain the overall reliability function of the power plant in terms of the component reliabilities.
This document provides an overview of key concepts in probability and statistics covered in Chapter 2, including:
- Sample spaces and events, which are the possible outcomes and subsets of outcomes for random experiments. Tree diagrams and Venn diagrams are used to represent these.
- Probability is interpreted and calculated for both discrete and continuous sample spaces using counting techniques like permutations and combinations.
- Rules for calculating probabilities of unions, intersections, and complements of events are discussed, along with concepts of conditional probability, independence, and Bayes' theorem.
- Random variables are briefly introduced as variables that may take on different values from a sample space.
The chapter aims to help students understand and apply these fundamental probability concepts.
Design of State Estimator for a Class of Generalized Chaotic Systemsijtsrd
In this paper, a class of generalized chaotic systems is considered and the state observation problem of such a system is investigated. Based on the time domain approach with differential inequality, a simple state estimator for such generalized chaotic systems is developed to guarantee the global exponential stability of the resulting error system. Besides, the guaranteed exponential decay rate can be correctly estimated. Finally, several numerical simulations are given to show the effectiveness of the obtained result. Yeong-Jeu Sun "Design of State Estimator for a Class of Generalized Chaotic Systems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29270.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/29270/design-of-state-estimator-for-a-class-of-generalized-chaotic-systems/yeong-jeu-sun
Solving practical economic load dispatch problem using crow search algorithm IJECEIAES
The document presents a crow search algorithm to solve the practical economic load dispatch problem considering valve-point loading effects and multiple fuel options. This problem is non-convex, non-smooth, and non-linear. The crow search algorithm is inspired by the intelligent social behavior of crows. It models the crows following each other to find food storage locations. The algorithm updates crow positions based on whether another crow detects it or not. Simulation results show the crow search algorithm finds high-quality solutions and performs effectively compared to other algorithms for solving the non-convex economic load dispatch problem.
Application of ann for ultimate shear strength of fly ash concrete beamseSAT Journals
Abstract
The application of artificial neural networks (ANN) for ultimate shear strength of fly ash concrete beams with transverse
reinforcement is investigated in this paper. An ANN model is built, trained and tested using the available test data of 216 RC beams
collected from the literature also the experimental data of twenty seven fly ash concrete beams under shear. The experimental shear
strength were also compared to those obtained using building codal equations and empirical equations proposed by various
researchers. The ANN model was found to predict satisfactorily when compared to available analytical predictions.
Keywords: Artificial Neural Network (ANN), Building codes, Comparison, Charts, Empirical Equations, Fly ash
Concrete, Shear Strength.
A comparative study of three validities computation methods for multimodel ap...IJECEIAES
The multimodel approach offers a very satisfactory results in modelling, diagnose and control of complex systems. In the modelling case, this approach passes by three steps: the determination of the model’s library, the validities computation and the establishment of the final model. In this context, this paper focuses on the elaboration of a comparative study between three recent methods of validities computation. Thus, it highlight the method that offers the best performances in term of precision. To achieve this goal, we apply, these three methods on two simulation examples in order to compare their performances.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam this is a multimedia exam
The only way I could do that was if you had to do a lot more work and then you would be done by yourself so you would be fine and then I could just go home to you if I needed you and you could just come over here or I can just go home if I need
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document outlines a group project on derivatives. It includes definitions of derivatives, a brief history of their development, and examples of applications in various fields such as automobiles, business, and mathematics. Rules for finding derivatives of sums, quotients, logarithmic, trigonometric, and exponential functions are also presented, along with examples of applying the rules to calculate derivatives.
The document discusses building human-based software estimation models that are accurate, intuitive, and easy to understand. It presents an approach using correlation and scale factors between estimated and actual effort. Experiments on a dataset of 178 samples show that combining correlation and scale factors into a decision tree achieves up to 93.3% accuracy. The resulting model bridges expert and algorithmic estimation methods.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
The document describes an experiment on flow system control using a PID controller. The objectives are to obtain the system characteristics like overshoot, rise time, settling time, period, and transport delay. It introduces PID controllers and how they work in a closed loop system using proportional, integral, and derivative modes. The apparatus section outlines the experimental setup, which uses a flow system with a square wave input and adjustable setpoint and proportional gain. Calculations are shown for analyzing the system response based on these parameters.
This document presents a multi-objective optimization model for integrated production and distribution scheduling. The objectives are to minimize total weighted tardiness and total distribution costs. A mixed integer programming formulation is developed with constraints for job precedence, vehicle capacity, and delivery times. A genetic algorithm using NSGA-II is proposed as a solution methodology, with chromosome representation, crossover, mutation and crowding distance calculation described. An example problem is presented to illustrate the model and solution approach.
Subject Title: Engineering Numerical Analysis
Subject Code: ID-302
Contents of this chapter:
Mathematical preliminaries,
Solution of equations in one variable,
Interpolation and polynomial Approximation,
Numerical differentiation and integration,
Initial value problems for ordinary differential equations,
Direct methods for solving linear systems,
Iterative techniques in Matrix algebra,
Solution of non-linear equations.
Approximation theory;
Eigen values and vector;
Modeling and implementation of a proportional derivative controller for elect...Alexander Decker
This document summarizes a research article that models and implements a proportional-derivative (P-D) controller for an electroviscous damper. The researchers developed a mathematical model of the damper system and used MATLAB to simulate the open-loop and closed-loop step responses. The results showed that the P-D controller reduced overshoot and settling time compared to just proportional control, with little effect on rise time and steady-state error. The controller successfully controlled the performance of the electroviscous damper.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
COMPARATIVE ANALYSIS OF CONVENTIONAL PID CONTROLLER AND FUZZY CONTROLLER WIT...IJITCA Journal
All the real systems exhibits non-linear nature,conventional controllers are not always able to provide good and accurate results. Fuzzy Logic Control is used to obtain better response. A model for simulation is designed and all the assumptions are made before the development of the model. An attempt has been made to analyze the efficiency of a fuzzy controller over a conventional PID controller for a three tank level control system using fuzzification & defuzzification methods and their responses are compared. Analysis is done through computer simulation using Matlab/Simulink toolbox. This study shows that the application of Fuzzy Logic Controller (FLC) gives the best response with triangular membership function and centroid defuzzification method.
This document presents a multi-objective optimization method for economic emission load dispatch (EELD) that considers economy, emissions, and transmission line security as objectives. The problem is formulated to minimize total fuel costs and emissions while maximizing line security for a power system. The multi-objective problem is converted to a single objective using goal attainment and then solved using simulated annealing. Results are presented for a 30-bus and 57-bus IEEE test case system to demonstrate the proposed method.
This document discusses evaluating reliability parameters for a power plant using algebra of logics. The power plant has two identical generators in standby redundancy to power four machines that can operate in pairs. The author develops a mathematical model representing the system configuration and operating conditions using Boolean logic. Equations are formulated to represent the conditions for successful operation of the power plant. The model is then solved using orthogonalization algorithms and algebra of logics to obtain the overall reliability function of the power plant in terms of the component reliabilities.
This document provides an overview of key concepts in probability and statistics covered in Chapter 2, including:
- Sample spaces and events, which are the possible outcomes and subsets of outcomes for random experiments. Tree diagrams and Venn diagrams are used to represent these.
- Probability is interpreted and calculated for both discrete and continuous sample spaces using counting techniques like permutations and combinations.
- Rules for calculating probabilities of unions, intersections, and complements of events are discussed, along with concepts of conditional probability, independence, and Bayes' theorem.
- Random variables are briefly introduced as variables that may take on different values from a sample space.
The chapter aims to help students understand and apply these fundamental probability concepts.
Design of State Estimator for a Class of Generalized Chaotic Systemsijtsrd
In this paper, a class of generalized chaotic systems is considered and the state observation problem of such a system is investigated. Based on the time domain approach with differential inequality, a simple state estimator for such generalized chaotic systems is developed to guarantee the global exponential stability of the resulting error system. Besides, the guaranteed exponential decay rate can be correctly estimated. Finally, several numerical simulations are given to show the effectiveness of the obtained result. Yeong-Jeu Sun "Design of State Estimator for a Class of Generalized Chaotic Systems" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-6 , October 2019, URL: https://www.ijtsrd.com/papers/ijtsrd29270.pdf Paper URL: https://www.ijtsrd.com/engineering/electrical-engineering/29270/design-of-state-estimator-for-a-class-of-generalized-chaotic-systems/yeong-jeu-sun
Solving practical economic load dispatch problem using crow search algorithm IJECEIAES
The document presents a crow search algorithm to solve the practical economic load dispatch problem considering valve-point loading effects and multiple fuel options. This problem is non-convex, non-smooth, and non-linear. The crow search algorithm is inspired by the intelligent social behavior of crows. It models the crows following each other to find food storage locations. The algorithm updates crow positions based on whether another crow detects it or not. Simulation results show the crow search algorithm finds high-quality solutions and performs effectively compared to other algorithms for solving the non-convex economic load dispatch problem.
Application of ann for ultimate shear strength of fly ash concrete beamseSAT Journals
Abstract
The application of artificial neural networks (ANN) for ultimate shear strength of fly ash concrete beams with transverse
reinforcement is investigated in this paper. An ANN model is built, trained and tested using the available test data of 216 RC beams
collected from the literature also the experimental data of twenty seven fly ash concrete beams under shear. The experimental shear
strength were also compared to those obtained using building codal equations and empirical equations proposed by various
researchers. The ANN model was found to predict satisfactorily when compared to available analytical predictions.
Keywords: Artificial Neural Network (ANN), Building codes, Comparison, Charts, Empirical Equations, Fly ash
Concrete, Shear Strength.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Build the Next Generation of Apps with the Einstein 1 Platform.
Rejoignez Philippe Ozil pour une session de workshops qui vous guidera à travers les détails de la plateforme Einstein 1, l'importance des données pour la création d'applications d'intelligence artificielle et les différents outils et technologies que Salesforce propose pour vous apporter tous les bénéfices de l'IA.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...shadow0702a
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELijaia
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Discover the latest insights on Data Driven Maintenance with our comprehensive webinar presentation. Learn about traditional maintenance challenges, the right approach to utilizing data, and the benefits of adopting a Data Driven Maintenance strategy. Explore real-world examples, industry best practices, and innovative solutions like FMECA and the D3M model. This presentation, led by expert Jules Oudmans, is essential for asset owners looking to optimize their maintenance processes and leverage digital technologies for improved efficiency and performance. Download now to stay ahead in the evolving maintenance landscape.
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...PriyankaKilaniya
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
3. Learning Objectives
After studying this chapter, you should be able to do the following:
1. Understanding and describe sample spaces and events for random experiments with graphs,
tables and tree diagram.
2. Interpret probabilities and use its outcomes to calculate probabilities of events in discrete
sample spaces.
3. Use permutations and combinations to count the number of outcomes in both an event and
the individual events.
4. Calculate the probabilities of joint events such as union and intersections from the
probabilities of individual events.
5. Interpret and calculate conditional probabilities of events.
6. Determine the independence of events and use independence to calculate probabilities.
7. Use Bayes’ theorem to calculate conditional probabilities
8. Understand random variables.
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4. Reference Book
Book: Applied Statistics and Probability for Engineers
“6th Edition”
Authors, Douglas C. Montgomery and George C. Runger.
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5. Course Contents
Chapter 1 The Role of Statistics in Engineering
Chapter 2 Probability
Chapter 3 Discrete Random Variables and Probability Distributions
Chapter 4 Continuous Random Variables and Probability Distributions
Chapter 5 Joint Probability Distributions
Chapter 8 Statistical Intervals for a Single Sample
Chapter 9 Tests of Hypotheses for a Single Sample
Revision
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6. Chapter Outline
❑Sample Spaces and Events
❑Random Experiments
❑Sample Spaces
❑Events
❑Counting Techniques
❑Addition Rules
❑Multiplication and Total Probability Rules
❑Independence
❑Bayes’ Theorem
❑Random Variables
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7. Sample Space and Events
Random Experiment
▪An experiment that can result in different outcomes, even though it is
repeated in the same manner every time, is called random experiment.
▪The set of all possible outcomes of a random experiment is called the
sample space of experiment and is denoted as 𝑺.
“A system designed without considering variation will be inadequate for practical use.”
“the sample space is defined according to the objective of analysis”
System
Input output
Controlled variables
System variables
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8. Presenting of Sample Space
1. 𝑺 = 𝑨, 𝑩, 𝑪, 𝑫, 𝑬, … . .
2. Tree diagram, such as the number of trails/experiment and the given outputs for each
trail/experiment.
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10. Illustrative examples
Example 2-1 Camera Flash
An experiment that selects a cell phone camera and records the recycle time of a flash (the time taken to
ready the camera for another flash). The possible values for this time is positive it is convenient to define the
sample space as simply the positive real numbers
𝑺 = 𝑹+
= 𝒙 𝒙 > 𝟎}
If it is known that all recycle times are between 1.5 and 5 seconds, the sample space can be
𝑺 = 𝑹+ = 𝒙 𝟏. 𝟓 < 𝒙 < 𝟓}
If the objective of the analysis is to consider only whether the recycle time is low, medium, or high, the
sample space can be taken to be the set of three outcomes
𝑺 = {𝒍𝒐𝒘, 𝒎𝒆𝒅𝒊𝒖𝒎, 𝒉𝒊𝒈𝒉}
If the objective of the analysis is only to evaluate whether or not a particular camera conforms to a minimum
recycle time specification, the sample space can be simplified to a set of two outcomes
𝑺 ={yes, no}
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11. Discrete and continuous sample spaces
A sample space is discrete if it consists of a finite or countable
infinite set of outcomes.
A sample space is continuous if it contains an interval.
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12. Example 2-3 Message Delays
Each message in a digital communication system is classified as to whether it is
received within the time specified by the system design. If three messages are
classified, use a tree diagram to represent the sample space of possible
outcomes.
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13. Example 2-4 Automobile Options
An automobile manufacturer provides vehicles equipped with selected options.
Each vehicle is ordered as:
• With or without an automobile transmission
• With or without a sunroof
• With one of three choices of a stereo system
• With one of four choices exterior colors
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14. Events
Event
An event is a subset of the sample space of a random experiment.
Basic set operations are:
• The union denoted as 𝐸1 ∪ 𝐸2
•The intersection denoted as 𝐸1 ∩ 𝐸2
•The complement denoted as 𝐸𝑐 or 𝑬′
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15. Example 2-8 Hospital Emergency Visits
Table below summarizes visits to emergency departments at four hospitals. People may leave
without being seen by a physician, and those visits are denoted as LWBS. The remaining visits
are serviced at the emergency department, and the visitor may or may not be admitted for a
stay in the hospital.
Let A denote the event that a visit is going to Hospital 1, 𝑨 = 𝟓𝟐𝟗𝟐 𝒗𝒊𝒔𝒕𝒐𝒓𝒔
B denote the event that the result of the visit is LWBS, 𝑩 = 𝟗𝟓𝟑 𝒗𝒊𝒔𝒕𝒐𝒓𝒔
Calculate the number of outcomes in 𝑨 ∩ 𝑩, 𝑨′
, 𝒂𝒏𝒅 𝑨 ∪ 𝑩.
𝑨 ∩ 𝑩 = 𝟏𝟗𝟓𝒗𝒊𝒔𝒕𝒐𝒓𝒔,
𝑨′ = 𝟐𝟐𝟐𝟓𝟐 − 𝟓𝟐𝟗𝟐 = 𝟏𝟔, 𝟔𝟗𝟎 𝒗𝒊𝒔𝒕𝒐𝒓𝒔, 𝑨 ∪ 𝑩 = 𝟓𝟐𝟗𝟐 + 𝟗𝟓𝟑 − 𝟏𝟗𝟓 = 𝟔𝟎𝟓𝟎𝒗𝒊𝒔𝒕𝒐𝒓𝒔,
Hospital
People Visited Hospital 1 Hospital 2 Hospital 3 Hospital 4 Total
LWBS 195 270 246 242 953 B
Admitted 1277 1558 666 984 4485
Not admitted 3820 5163 4728 3103 16814
Total 5292 A 6991 5640 4329 22252
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195
16. Mutually Exclusive Events
Two events, denoted as 𝑬𝟏 𝒂𝒏𝒅 𝑬𝟐, such that
𝑬𝟏 ∩ 𝑬𝟐 = ∅ are said to be mutually exclusive events.
•The complement of an event: (𝑬′)′ = 𝑬
•The distributive law for set operations implies that:
𝑨 ∪ 𝑩 ∩ 𝑪 = (𝑨 ∩ 𝑪) ∪ (𝑩 ∩ 𝑪) and 𝑨 ∩ 𝑩 ∪ 𝑪 = 𝑨 ∪ 𝑪 ∩ 𝑩 ∪ 𝑪
•DeMorgan’s laws imply that: (𝑨 ∪ 𝑩)′= 𝑨′ ∩ 𝑩′ and (𝑨 ∩ 𝑩)′=𝑨′ ∪ 𝑩′
•And also, 𝑨 ∩ 𝑩 = 𝑩 ∩ 𝑨 and 𝑨 ∪ 𝑩 = 𝑩 ∪ 𝑨
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19. Counting Techniques
Multiplication Rule:-
Assume an operation can be described as a sequence of 𝑘 steps, and
◦ The number of ways of completing step 1 is 𝑛1, and
◦ The number of ways of completing step 2 is 𝑛2 for each way of completing
step 1, and
◦ The number of ways of completing step 3 is 𝑛3 for each way of completing
step 2, and so forth.
The total number of ways of completing the operation is
𝒏𝟏 × 𝒏𝟐 × ⋯ × 𝒏𝒌
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20. Permutation
Consider a set of elements, such as 𝑺 = 𝒂, 𝒃, 𝒄
So the orders of elements may be have the permutation as
𝒂𝒃𝒄, 𝒃𝒂𝒄, 𝒄𝒃𝒂, 𝒃𝒄𝒂, 𝒂𝒄𝒃, 𝒂𝒏𝒅 𝒄𝒂𝒃
The number of permutations = 𝟑 × 𝟐 × 𝟏 = 𝟑!
So
The number of permutations of 𝒏 different elements
= 𝒏 × 𝒏 − 𝟏 × 𝒏 − 𝟐 × ⋯ × 𝟐 × 𝟏 = 𝒏!
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21. Permutation of Subsets
The number of permutations of subsets of 𝒓 elements selected from a set of 𝒏 different
elements is written as 𝑷𝒓
𝒏
𝑷𝒓
𝒏 =
𝒏!
(𝒏−𝒓)!
Example 2-10 Printed Circuit Board, A printed circuit board has eight different
locations in which a component can be placed. If four different components are
to be placed on the board, how many different designs are possible?
𝑷𝒓
𝒏
= 𝟖 × 𝟕 × 𝟔 × 𝟓 =
𝟖!
𝟒!
= 1680 different designs are possible
1 2 3 4 5 6 7 8
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22. Permutation of Similar Objects
The number of permutations of 𝒏 = 𝒏𝟏 + 𝒏𝟐 + ⋯ + 𝒏𝒓 objects of which 𝒏𝟏are of
one type, 𝒏𝟐 are of a second type,…, and 𝒏𝒓 are of an 𝒓th type is
𝒏!
𝒏𝟏!𝒏𝟐!𝒏𝟑!…𝒏𝒓!
Example 2-11 Hospital Schedule, A hospital operating room needs to schedule
three knee surgeries and two hip surgeries in a day. We denote a knee and hip
surgery as k and h, respectively. The number of possible sequences of three knee
and two hip surgeries is
𝟓!
𝟑!𝟐!
= 𝟏𝟎
The 10 sequences are easily summarized:
{kkkhh ,kkhkh ,kkhhk, khkkh, khhkk, khhkk, hkkkh, hkkhk, hkhkk, hhkkk}
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23. Combinations “Without order consideration”
Is the number of subsets of r elements that can be selected from a
set of n elements is denoted as
𝑛
𝑟
or 𝐶𝑟
𝑛
“Without order consideration”
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𝐶𝑟
𝑛=
𝑛
𝑟
=
𝑛!
𝑟! (𝑛 − 𝑟)!
24. Examples
Example 2-13 Printed Circuit Board Layout
A printed circuit has 8 different locations in which a component can be placed.
If 5 identical components are to be placed on the board, how many different
designs are possible?
Solution
Each design is a subset of size five from the eight locations that are to contain
the components so using the following equation for combinations
𝐶𝑟
𝑛
=
𝑛
𝑟
=
𝑛!
𝑟!(𝑛−𝑟)!
𝑪𝒓
𝒏=
𝟖
𝟓
=
𝟖!
𝟓!(𝟖−𝟓)!
= 56 designs
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27. Mutually Exclusive Events
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In general, a collection of events, 𝑬𝟏, 𝑬𝟐, 𝑬𝟑,…., 𝑬𝒌, is said to be
mutually exclusive if there is no overlap (intersect) among of them.
Mutually Exclusive Events
A collection of events, 𝑬𝟏, 𝑬𝟐, 𝑬𝟑,…., 𝑬𝒌, is said to be mutually
exclusive if for all pairs,
𝑬𝟏 ∩ 𝑬𝒋 = ∅
So, the addition rule is
𝑷 𝑬𝟏 ∪ 𝑬𝟐∪ 𝑬𝟑 ∪ …. ∪ 𝑬𝒌 = 𝑷(𝑬𝟏)+P( 𝑬𝟐)+…. 𝑷(𝑬𝒌)
28. Conditional Probability
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𝑷 𝑺𝒖𝒏𝒏𝒚 𝑨𝑵𝑫 𝑪𝒍𝒐𝒖𝒅𝒚 = 𝑷 𝑺𝒖𝒏𝒏𝒚 ∗ 𝑷(𝑪𝒍𝒐𝒖𝒅𝒚/𝑺𝒖𝒏𝒏𝒚)
𝑷 𝑺𝒖𝒏𝒏𝒚 ∩ 𝑪𝒍𝒐𝒖𝒅𝒚 = 𝑷 𝑺𝒖𝒏𝒏𝒚 ∗ 𝑷(𝑪𝒍𝒐𝒖𝒅𝒚/𝑺𝒖𝒏𝒏𝒚)
Sunny
Not
Sunny
50%
50%
Cloudy
Dusty
30%
70%
Cloudy
Rainy
40%
60%
𝑃(𝑪𝒍𝒐𝒖𝒅𝒚/𝑺𝒖𝒏𝒏𝒚)
𝑃(𝑪𝒍𝒐𝒖𝒅𝒚/𝑵𝒐𝒕 𝑺𝒖𝒏
The Conditional Probability
The Conditional Probability of an event B given
an event A, denoted as P(B/A), is
Probability of B given A, is P(B/A)
P(B/A)=𝑷(𝑨 ∩ 𝑩)/𝑷(𝑨) for P(A)>0
29. Assignment 2
Represent the outcomes of these experiments:
1. The tossing of coin twice,
2. The passing of you in your exams in four
subjects
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