This course focuses on the fundamentals of probability and statistics which are used in various research areas such as model for digital communication, analysis of genome, and statistical analysis of big data. This course provides not only mathematical foundation of probability and statistics, but also practical methods to apply these mathematical knowledge.
At the end of this course, students will be able to understand the following concepts:
1) The probability theory (probability axioms, expected value, variance, and moment generating function)
2) Multidimensional probability distribution, statistical independence, and correlation
3) Normal distribution and binomial distribution
4) Law of large numbers and central limit theorem
5) Hypothesis testing, point estimation, interval estimation
6) Bayesian statistics
probability axioms, expected value, variance, moment generating function, multidimensional probability distribution, statistical independence, correlation, normal distribution, binomial distribution, law of large numbers, central limit theorem, hypothesis testing, point estimation, interval estimation, Bayesian statistics
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Towards the end of class, students are given exercise problems related to what is taught on that day to solve. In the exercise class, students are given advanced or practical problems related to the previous lecture classes.
Course schedule | Required learning | |
---|---|---|
Class 1 | Lecture 1: Basic mathematical knowledge | Peruse chapter 1 of the textbook. |
Class 2 | Lecture 2: Definition of probability | Peruse chapter 2 of the textbook. |
Class 3 | Exercise 1 | Review Lectures 1 and 2. |
Class 4 | Lecture 3: Bayes' theorem and random variables | Peruse the first half of chapter 3 of the textbook. |
Class 5 | Lecture 4: Random variables 2 | Peruse the last half of chapter 3 of the textbook. |
Class 6 | Exercise 2 | Review Lectures 3 and 4 |
Class 7 | Lecture 5: Multi-dimensional random variable | Peruse the last half of chapter 3 of the textbook. |
Class 8 | Lecture 6: Binomial distribution and Poisson distribution | Peruse the first half of chapter 4 of the textbook. |
Class 9 | Exercise 3 | Review Lectures 5 and 6 |
Class 10 | Lecture 7: Normal distribution and central limit theorem | Peruse the last half of chapter 4 of the textbook. |
Class 11 | Lecture 8: Distribution of samples and statistics | Peruse the first half of chapter 5 of the textbook. |
Class 12 | Exercise 4 | Review Lectures 1 through 7. |
Class 13 | Lecture 9: Normal population | Peruse the last half of chapter 5 of the textbook. |
Class 14 | Exercise 5 | Review Lectures 8 and 9 |
Class 15 | Lecture 10: Statistical estimation | Peruse Section 6.1 of the textbook. |
Class 16 | Lecture 11: Interval estimation and confidence level | Peruse Section 6.2 of the textbook. |
Class 17 | Exercise 6 | Review Lectures 10 and 11 |
Class 18 | Lecture 12: Interval estimation 2 | Peruse Section 6.2 of the textbook. |
Class 19 | Lecture 13: Hypothesis testing | Peruse Section 6.3 of the textbook. |
Class 20 | Exercise 7 | Review Lectures 12 and 13 |
Class 21 | Lecture 14: Hypothesis testing2 | Peruse Sections 6.4 and 6.5 of the textbook. |
Class 22 | Lecture 15: Review | Review all Lectures |
Class 23 | Exercise 8 | Review all Lectures |
Junkichi Satsuma, Probability and Statistics, Iwanami, 1989. (Japanese)
All materials used in class can be found on OCW-i.
Student learning outcomes are evaluated by the results of exercises (20%), small examinations (40%), and the final examination (40%).
No prerequisites.