We conduct in-person (face-to-face) classes in Spring 2022. Those who are based abroad and who wish take the classes online
should contact the lecturer via email.
This course introduces basic concepts of probability and statistics through discussions on the theory and applications. The students will learn fundamental notions of probability such as conditional probability, independence, probability distributions, random variables, expectation, law of large numbers, as well as useful statistical methods such as bootstrapping, maximum likelihood estimators, confidence intervals, and hypotheses testing.
This course introduces basic concepts of probability and statistics through discussions on the theory and applications. The students will learn fundamental notions of probability such as conditional probability, independence, probability distributions, random variables, expectation, law of large numbers, as well as useful statistical methods such as bootstrapping, maximum likelihood estimators, confidence intervals, and hypotheses testing.
This class is intended to equip students with basic knowledge and skills of probability and statistics used in science and
engineering fields.
| Goals and objectives | Course Outcomes | |
|---|---|---|
| 1. | Students will be able to learn fundamental notions of probability such as probability distributions, conditional probability, law of large numbers. |
A-1
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| 2. | Students will be able to compute probability of events, expectation, variance, covariance, and correlations involving discrete and continuous random variables. |
A-1
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| 3. | Students will be able to use bootstrapping, maximum likelihood, and least square estimators. |
A-1
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| 4. | Students will be able to learn exploratory data analysis, sample-size selection for statistical inference, and methods of hypothesis testing as well as their limitations. |
A-1
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| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Discussion on applications of probability and statistics; Outcomes, events, and probability | Review Chapters 1 and 2 in the textbook | 190分 |
| 2. | Independence; Conditional probability; Bayes’ rule | Review Chapter 3 in the textbook (Homework assignment) | 190分 |
| 3. | Discrete random variables; Probability distributions; Probability mass functions; Discrete-uniform, binomial distributions |
Review Chapter 4 in the textbook | 190分 |
| 4. | Continuous random variables; Cumulative distribution and probability density functions; Uniform, exponential, pareto, and normal distributions |
Review Chapter 5 in the textbook (Homework assignment) | 190分 |
| 5. | Expectation and variance; Simulation and computation with random variables | Review Chapter 7, Sections 6.2, 8.1, 8.2 in the textbook | 190分 |
| 6. | Joint distributions; Covariance and correlation | Review Chapters 9 and 10 in the textbook (Homework assignment) | 190分 |
| 7. | Law of large numbers, central limit theorem, and some of their applications | Review Sections 13.1-13.3, 14.1, 14.2 in the textbook | 190分 |
| 8. | Exploratory data analysis; Sampling; empirical distribution; Basic statistical models | Review Sections 15.3, 16.1-16.4, 17.1-17.4 in the textbook (Homework assignment) | 190分 |
| 9. | Bootstrap methods; Estimates and estimators | Review Sections 18.1, 18.2, Chapter 19 in the textbook | 190分 |
| 10. | Maximum likelihood and least square estimators | Review Chapters 21 and 22 in the textbook (Homework assignment) | 190分 |
| 11. | Confidence intervals; Choice of sample size | Review Chapter 24 in the textbook | 190分 |
| 12. | Hypotheses testing; P-Values; Type I and Type II errors; t-test | Review Sections 25.1-25.3, 27.1,27.2 (Homework assignment) | 190分 |
| 13. | Discussions on applications of statistical methods | Review Sections 28.1-28.4 | 190分 |
| 14. | Final exam and discussions on the solutions afterwards | Preparation for final | 190分 |
| Total. | - | - | 2660分 |
| Homework | Final | Total. | |
|---|---|---|---|
| 1. | 15% | 15% | 30% |
| 2. | 15% | 5% | 20% |
| 3. | 15% | 5% | 20% |
| 4. | 15% | 15% | 30% |
| Total. | 60% | 40% | - |
Homework reports will contribute to 60% of the grade; Final exam will contribute to 40% of the grade.
Those who get at least 60% of the full score will pass this course.
Those who get at least 60% of the full score will pass this course.
A Modern Introduction to Probability and Statistics: Understanding Why and How, F. M. Dekking, C. Kraaikamp, H. P. Lopuhaä,
L. E. Meester, Springer, 2010.
- By appointment. Contact e-mail address: ahmet@shibaura-it.ac.jp
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Fri Sep 23 04:03:37 JST 2022