| Course title | |||||
| 数理統計学 [Mathematical Statistics] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 1st | |
| Course type | 1st | Course code | 022201 | ||
| Instructor(s) | |||||
| 勝島 義史 [KATSUSHIMA Yoshifumi] | |||||
| Facility affiliation | Graduate School of Engineering | Office | Email address | ||
| Course description |
| In this class, we learn probability in a half of the course first, and later we learn statistics. The aims of this course are to learn ‘‘expected values’’ and ‘‘variances’’ of random variables, classical distributions, the proof of ‘‘Law of Large Numbers’’ and ‘‘central limit theorem’’ in a class of probability, and in a class of statistics, we will learn ‘‘estimations’’ of some statistical values, the method of ‘‘hypothesis testing’’, and ‘‘linear regressions’’. |
| Expected Learning |
|
1. You can calculate some expected values and variances of easy random variables. 2. You understand some characters of classical distributions. 3. You can estimate width of values by using central limit theorem or Law of Large Numbers. 4. You can estimate some statistical values by a method of point estimation and a method of section estimation. 5. You can say that some propositions about the statistical values are ‘almost true’ or ‘almost false’ by a method of hypothesis testing. |
| Course schedule |
|
The following schedule is not so rigid. I will change some topics and orders, but I want to talk these topics. 1. Guidance, from combinations to probabilities. 2. The definition of probability spaces and random values. 3. Expected values, variances, and generating functions. 4. Classical distributions and their characters: uniform, binomial, Poisson, exponential, Gamma, normal, and logarithmic normal distributions, etc. I will talk 2 or 3 classes about this topic. 5. The Chebyshev’s inequality and the Law of Large Number theorem. 6. A proof of central limit theorem. 7. An introduction of the Monte Carlo method by using a computer language ‘R’ or ‘Fortran’ (they are free software of numerical calculating, especially, R is a language for calculating statistical objects). 8. The definition of the statistical values. 9. A point estimating method, a maximum likelihood estimation method. 10. A section estimation. 11. A hypothesis testing. 12. The least squares method and a linear regression. 13. Examination. |
| Prerequisites |
| You should be familiar with analysis (multi-variable Calculus of differentials/integrals) and linear algebra. |
| Required Text(s) and Materials |
|
The following book is a textbook of this class: Kakutitsu-toukei no kiso, MATSUMOTO Hiroyuki, Gakujutsu-tosho-shuppann (in Japanese) This book includes normal topics briefly, so I will recommend this book as a textbook, but you may read other books. I hope you read at least one book about the mathematical statistics or probabilities. |
| References |
|
The following textbooks are popular in Japan: 1. Toukei-gaku-nyumonn (An introduction of statistics) (kiso-toukeigaku I), Tokyo-daigaku-kyouyou-gakubu-toukeigaku-kyoshitsu, Tokyo-daigaku-shuppann 2. Tokyo-daigaku-kougaku-kyoutei kiso-kei suugaku kakuritsu-toukei I, NAWATA Kazumitsu, Maruzen-shuppann The following books are for an introduction to a numerical calculation of statistics by using computers. You should learn numerical calculations by yourself to compute some statistical values. 3. Hajimete-no-R, MURAI Jun-ichiro, Kitaohji-shobou 4. Excel ni yoru toukei-nyumonn -Excel2007 taiou-, NAWATA Kazumitsu, Asakura-shoten And one more book for undergraduate students who are not so vigorous to study. This book will show you a calculus, but does not contain exact proofs or definitions. However, this book is nice for reading. I like SATSUMA-san. 5. Rikoukei-no-suugaku-nyumonn-course7 kakuritsu-toukei, SATSUMA Junkichi, Iwanami-shoten |
| Assessment/Grading |
|
Examination 100%. You may bring and use textbooks, notes, calculators and computers to the classroom of the examination. |
| Message from instructor(s) |
| Just do it. It is not clear until you have done it. |
| Course keywords |
| Probability, Statistics |
| Office hours |
| There is no office for me in TUAT, so that there does not exist any office hours. You may ask me some questions in the classroom, or you may ask me some questions by E-MAIL. My E-MAIL address will be told during the first class. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/22/2019 6:30:47 PM |