With 80 steps Galton boards, we can see the binomial distribution approximated to the normal distribution.
Youtube ===>>>
https://www.youtube.com/watch?v=3w4e1RQTAB8
A periodic signal repeats its pattern over a specific time interval and can be represented by a mathematical equation, while an aperiodic signal does not repeat over time and cannot be determined with certainty at any given point or represented by an equation. Examples of periodic signals include sine, cosine, and square waves, while aperiodic signals include sound from radios and noise.
This document provides an overview of signals and systems. It defines key terms like signal, system, continuous and discrete time signals, analog and digital signals, periodic and aperiodic signals. It also discusses different types of signals like deterministic and probabilistic signals, energy and power signals. The document then classifies systems as linear/nonlinear, time-invariant/variant, causal/non-causal, and with/without memory. It provides examples of different signals and properties of signals like magnitude scaling, time shifting, reflection and scaling. Overall, the document introduces fundamental concepts in signals and systems.
Static modeling represents the static elements of software such as classes, objects, and interfaces and their relationships. It includes class diagrams and object diagrams. Class diagrams show classes, attributes, and relationships between classes. Object diagrams show instances of classes and their properties. Dynamic modeling represents the behavior and interactions of static elements through interaction diagrams like sequence diagrams and communication diagrams, as well as activity diagrams.
A signal is a pattern of variation that carry information.
Signals are represented mathematically as a function of one or more independent variable
basic concept of signals
types of signals
system concepts
This document discusses signals and systems. It begins with an introduction that signals arise in many areas like communications, circuit design, etc. and a signal contains information about some phenomenon. A system processes input signals to produce output signals.
It then discusses different types of signals like continuous-time and discrete-time signals. Deterministic signals can be written mathematically while stochastic signals cannot. Periodic signals repeat and aperiodic signals do not. Even and odd signals have specific properties related to their symmetry.
Operations on signals are also covered, including addition, multiplication by a constant, multiplication of two signals, time shifting which delays or advances a signal, and time scaling which compresses or expands a signal. Common signal models
With 80 steps Galton boards, we can see the binomial distribution approximated to the normal distribution.
Youtube ===>>>
https://www.youtube.com/watch?v=3w4e1RQTAB8
A periodic signal repeats its pattern over a specific time interval and can be represented by a mathematical equation, while an aperiodic signal does not repeat over time and cannot be determined with certainty at any given point or represented by an equation. Examples of periodic signals include sine, cosine, and square waves, while aperiodic signals include sound from radios and noise.
This document provides an overview of signals and systems. It defines key terms like signal, system, continuous and discrete time signals, analog and digital signals, periodic and aperiodic signals. It also discusses different types of signals like deterministic and probabilistic signals, energy and power signals. The document then classifies systems as linear/nonlinear, time-invariant/variant, causal/non-causal, and with/without memory. It provides examples of different signals and properties of signals like magnitude scaling, time shifting, reflection and scaling. Overall, the document introduces fundamental concepts in signals and systems.
Static modeling represents the static elements of software such as classes, objects, and interfaces and their relationships. It includes class diagrams and object diagrams. Class diagrams show classes, attributes, and relationships between classes. Object diagrams show instances of classes and their properties. Dynamic modeling represents the behavior and interactions of static elements through interaction diagrams like sequence diagrams and communication diagrams, as well as activity diagrams.
A signal is a pattern of variation that carry information.
Signals are represented mathematically as a function of one or more independent variable
basic concept of signals
types of signals
system concepts
This document discusses signals and systems. It begins with an introduction that signals arise in many areas like communications, circuit design, etc. and a signal contains information about some phenomenon. A system processes input signals to produce output signals.
It then discusses different types of signals like continuous-time and discrete-time signals. Deterministic signals can be written mathematically while stochastic signals cannot. Periodic signals repeat and aperiodic signals do not. Even and odd signals have specific properties related to their symmetry.
Operations on signals are also covered, including addition, multiplication by a constant, multiplication of two signals, time shifting which delays or advances a signal, and time scaling which compresses or expands a signal. Common signal models
Derivative of sine function: A graphical explanationHideo Hirose
The derivative of a sine function can be derived by using the limit for sine function. However, it seems difficult to understand this transformation. Thus, I have drawn a figure expressing the differentiation.
sine関数微分 d sin x / dx = cos x の説明は、sineの差の公式を積に変換して、sin x / x → 1 (x → 0) を使って説明されることが多い。
ここでは、図形的に示してみた。sin x / x → 1 (x → 0) が見えないだけになっているが、結局は、、、
Success/Failure Prediction for Final Examination using the Trend of Weekly On...Hideo Hirose
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help regulate emotions and stress levels.
Attendance to Lectures is Crucial in Order Not to Drop OutHideo Hirose
H. Hirose, Attendance to Lectures is Crucial in Order Not to Drop Out, 7th International Conference on Learning Technologies and Learning Environments (LTLE2018), pp.194-198, July 8-12, 2018.
How many times are we tossing coins until we observe head, tail, and head? It's ten. It's not eight. This is an intriguing result against our intuition.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Different classification results under different criteria, distance and proba...Hideo Hirose
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Interesting but difficult problem: find the optimum saury layout on a gridiro...Hideo Hirose
Even though we use a simple but ridiculous problem finding the optimum saury baking layout on a fish gridiron by Joule heat, we can invoke the interest to science by combining electrical engineering, linear algebra and probability viewpoints. These elements are, use of solving linear equation and Poisson's equation, and applying the central limit theorem to this situation. In addition, by removing the constraints, we can create a new problem free from our common sense. Presenting funny but essential problems could be another aspect for active learning using the problem of the interdisciplinary scientific methods.
The cumulative exposure model (CEM) is often used to express the failure probability model in the step-up test method; the step-up procedure continues until a breakdown occurs. This probability model is widely accepted in reliability fields because accumulation of fatigue is considered to be reasonable. Contrary to this, the memoryless model (MM) is also used in electrical engineering because accumulation of fatigue is not observed in some cases. We propose here a new model, the extended cumulative exposure model (ECEM), which includes features of both the described models. A simulation study and an application to the actual experimental case of oil insulation test support the validity of the proposed model. The independence model (IM) is also discussed.
Parameter estimation for the truncated weibull model using the ordinary diffe...Hideo Hirose
In estimating the number of failures using the truncated data for the Weibull model, we often encounter a case that the estimate is smaller than the true one when we use the likelihood principle to conditional probability. In infectious disease predictions, the SIR model described by simultaneous ordinary differential equations are often used, and this model can predict the final stage condition, i.e., the total number of infected patients, well, even if the number of observed data is small. These two models have the same condition for the observed data: truncated to the right. Thus, we have investigated whether the number of failures in the Weibull model can be estimated accurately using the ordinary differential equation. The positive results to this conjecture are shown.
This document summarizes Hideo Hirose's presentation on trunsored data analysis at the IEEE Reliability Society Japan Chapter Annual Meeting. Hirose discusses different types of incomplete data including censored, truncated, and trunsored (mixture) data. He presents likelihood functions for censored, truncated, and mixture models. Hirose also provides an example analysis of failure time data using censored, truncated, and mixture models. He notes that while parameter estimates can be obtained from the mixture model, confidence intervals are not straightforward, especially when p is near 1. Hirose discusses approaches for hypothesis testing when p is near 1 where the data could be assumed censored.
An accurate ability evaluation method for every student with small problem it...Hideo Hirose
To enhance the chance of use of the item response theory (IRT) in universities, we developed a test evaluation system via the Web for university teachers, and we have been evaluating students' abilities by using the IRT system in midterm and final examinations for two years.
We show a surprising aspect regarding the adoption of the IRT system in university tests. That is, the IRT can not only give us the problem difficulty information but also can provide the accurate student ability evaluation, even if the number of problems is small. Therefore, we can include high and low level test items together so that we can assess a variety of students' abilities accurately and fairly; we do not worry about providing easier problems that will make the lecture level decline; in other words, we do not care about finding the most appropriate problem levels to each student. We can provide all level problems uniformly distributed to all students, and we can still assess the students' abilities accurately. Consequently, students do not raise claims about their scores; they seem to be satisfied with it.
We show these results, in this paper, by a theoretical background, a simulation study, and our empirical results.
Derivative of sine function: A graphical explanationHideo Hirose
The derivative of a sine function can be derived by using the limit for sine function. However, it seems difficult to understand this transformation. Thus, I have drawn a figure expressing the differentiation.
sine関数微分 d sin x / dx = cos x の説明は、sineの差の公式を積に変換して、sin x / x → 1 (x → 0) を使って説明されることが多い。
ここでは、図形的に示してみた。sin x / x → 1 (x → 0) が見えないだけになっているが、結局は、、、
Success/Failure Prediction for Final Examination using the Trend of Weekly On...Hideo Hirose
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help regulate emotions and stress levels.
Attendance to Lectures is Crucial in Order Not to Drop OutHideo Hirose
H. Hirose, Attendance to Lectures is Crucial in Order Not to Drop Out, 7th International Conference on Learning Technologies and Learning Environments (LTLE2018), pp.194-198, July 8-12, 2018.
How many times are we tossing coins until we observe head, tail, and head? It's ten. It's not eight. This is an intriguing result against our intuition.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Different classification results under different criteria, distance and proba...Hideo Hirose
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Interesting but difficult problem: find the optimum saury layout on a gridiro...Hideo Hirose
Even though we use a simple but ridiculous problem finding the optimum saury baking layout on a fish gridiron by Joule heat, we can invoke the interest to science by combining electrical engineering, linear algebra and probability viewpoints. These elements are, use of solving linear equation and Poisson's equation, and applying the central limit theorem to this situation. In addition, by removing the constraints, we can create a new problem free from our common sense. Presenting funny but essential problems could be another aspect for active learning using the problem of the interdisciplinary scientific methods.
The cumulative exposure model (CEM) is often used to express the failure probability model in the step-up test method; the step-up procedure continues until a breakdown occurs. This probability model is widely accepted in reliability fields because accumulation of fatigue is considered to be reasonable. Contrary to this, the memoryless model (MM) is also used in electrical engineering because accumulation of fatigue is not observed in some cases. We propose here a new model, the extended cumulative exposure model (ECEM), which includes features of both the described models. A simulation study and an application to the actual experimental case of oil insulation test support the validity of the proposed model. The independence model (IM) is also discussed.
Parameter estimation for the truncated weibull model using the ordinary diffe...Hideo Hirose
In estimating the number of failures using the truncated data for the Weibull model, we often encounter a case that the estimate is smaller than the true one when we use the likelihood principle to conditional probability. In infectious disease predictions, the SIR model described by simultaneous ordinary differential equations are often used, and this model can predict the final stage condition, i.e., the total number of infected patients, well, even if the number of observed data is small. These two models have the same condition for the observed data: truncated to the right. Thus, we have investigated whether the number of failures in the Weibull model can be estimated accurately using the ordinary differential equation. The positive results to this conjecture are shown.
This document summarizes Hideo Hirose's presentation on trunsored data analysis at the IEEE Reliability Society Japan Chapter Annual Meeting. Hirose discusses different types of incomplete data including censored, truncated, and trunsored (mixture) data. He presents likelihood functions for censored, truncated, and mixture models. Hirose also provides an example analysis of failure time data using censored, truncated, and mixture models. He notes that while parameter estimates can be obtained from the mixture model, confidence intervals are not straightforward, especially when p is near 1. Hirose discusses approaches for hypothesis testing when p is near 1 where the data could be assumed censored.
An accurate ability evaluation method for every student with small problem it...Hideo Hirose
To enhance the chance of use of the item response theory (IRT) in universities, we developed a test evaluation system via the Web for university teachers, and we have been evaluating students' abilities by using the IRT system in midterm and final examinations for two years.
We show a surprising aspect regarding the adoption of the IRT system in university tests. That is, the IRT can not only give us the problem difficulty information but also can provide the accurate student ability evaluation, even if the number of problems is small. Therefore, we can include high and low level test items together so that we can assess a variety of students' abilities accurately and fairly; we do not worry about providing easier problems that will make the lecture level decline; in other words, we do not care about finding the most appropriate problem levels to each student. We can provide all level problems uniformly distributed to all students, and we can still assess the students' abilities accurately. Consequently, students do not raise claims about their scores; they seem to be satisfied with it.
We show these results, in this paper, by a theoretical background, a simulation study, and our empirical results.
5. Marilynへのアカデミアからの初期の反応
あああっ、自分の解答は誤答の方だった.
このような誤答を正しいと思い,示された正答をいつまでも信じられない君,そん
なに悩むことはない.実は,Marilynからの解答が提示された初期,Marilynへのア
カデミアからの反応はさんざんだったのだから.
Let me explain. If one door is shown to be a loser, that information
changes the probability of either remaining choice, neither of which has
any reason to be more likely, to 1/2. As a professional mathematician, I’m
very concerned with the general public’s lack of mathematical skills.
Please help by confessing your error and in the future being more careful.
AAA BBB, Ph.D.
CCC DDD University
You blew it, and you blew it big! Since you seem to have difficulty
grasping the basic principle at work here, I’ll explain. After the host
reveals a goat, you now have a one-in two chance of being correct.
Whether you change your selection or not, the odds are the same.
There is enough mathematical illiteracy in this country, and we don’t
need the holder of the world’s highest l.Q. propagating more. Shame!
EEE FFF, Ph.D.
GGG HHH University
というように続々と続いた.