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: Definition of probability and conditional probability||Peruse chapters 1 and 2 of the textbook.|
|Class 2||Exercise 1||Review Lecture 1.|
|Class 3||Lecture 2:Bayes' theorem and random variables||Peruse the latter half of chapter 2 and the first half of chapter 3 of the textbook.|
|Class 4||Lecture 3: Random variables 2||Peruse the last half of chapter 3 of the textbook.|
|Class 5||Exercise 2||Review Lectures 2 and 3.|
|Class 6||Lecture 4: Multi-dimensional random variable||Peruse the last half of chapter 3 of the textbook.|
|Class 7||Lecture 5: Binomial distribution and Poisson distribution||Peruse the first half of chapter 4 of the textbook.|
|Class 8||Exercise 3||Review Lectures 4 and 5.|
|Class 9||Lecture 6: Normal distribution and central limit theorem||Peruse the last half of chapter 4 of the textbook.|
|Class 10||Mid-term examination||Review Lectures 1-6.|
|Class 11||Lecture 7: Distribution of samples and statistics||Peruse the first half of chapter 5 of the textbook.|
|Class 12||Exercise 4||Review Lecture 7 .|
|Class 13||Lecture 8: Normal population||Peruse the last half of chapter 5 of the textbook.|
|Class 14||Lecture 9: Statistical estimation||Peruse Section 6.1 of the textbook.|
|Class 15||Exercise 5||Review Lectures 8 and 9.|
|Class 16||Lecture 10: Interval estimation and confidence level||Peruse Section 6.2 of the textbook.|
|Class 17||Lecture 11: Interval estimation 2||Peruse Section 6.2 of the textbook.|
|Class 18||Exercise 6||Review Lectures 10 and 11.|
|Class 19||Lecture 12: Hypothesis testing||Peruse Sections 6.3, 6.4 and 6.5 of the textbook.|
|Class 20||Exercise 7||Review Lecture 12.|
|Class 21||End-term examination||Review Lectures 7-12.|
To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.
Junkichi Satsuma, Probability and Statistics, Iwanami, 2019. (Japanese)
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%).