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PROBABILITY[DS1]
| Lecturer(s) | SAKAI, SHOTARO |
|---|---|
| Credit(s) | 2 |
| Academic Year/Semester | 2026 Spring |
| Day/Period | Mon.2 |
| Campus | SFC |
| Class Format | Face-to-face classes (conducted mainly in-person) |
| Registration Number | 07979 |
| Faculty/Graduate School | POLICY MANAGEMENT / ENVIRONMENT AND INFORMATION STUDIES |
| Year Level | 1, 2, 3, 4 |
| Field | FUNDAMENTAL SUBJECTS SUBJECTS OF DATA SCIENCE DATA SCIENCE 1 |
| Grade Type | This item will appear when you log in (Keio ID required). |
| English Support | Without English Support |
| Related Classes | B3101 統計基礎/INTRODUCTION TO STATISTICS B3103 微分・積分/CALCULUS B3104 線形代数/LINEAT ALGEBRA |
| Location | SFC |
| Course Requirements | This item will appear when you log in (Keio ID required). |
Student Screening *For conditions regarding "additional permission", please refer to the "Student Screening Details" section. Approval for additional permission is at the lecturer's discretion, and is not guaranteed. | This item will appear when you log in (Keio ID required). |
Screening Method *If selection is by lottery: Complete the course registration process and check your permission status on the course registration screen. If selection is by assignment: Carefully review the "Student Screening Details" section, register for the course via the "Assignment Submission URL," and submit the required assignment. | This item will appear when you log in (Keio ID required). |
| Expected Number of Acceptances | This item will appear when you log in (Keio ID required). |
| Contact(Mail) | This item will appear when you log in (Keio ID required). |
| Course Description | Students learn statistical science, modelling and simulation to develop mathematical reasoning skills applicable to data analysis and decision making in a variety of fields. |
| K-Number | FPE-CO-03013-211-12 |
| Course Administrator | Faculty/Graduate School | FPE | POLICY MANAGEMENT / ENVIRONMENT AND INFORMATION STUDIES |
|---|---|---|---|
| Department/Major | CO | ||
| Main Course Number | Level | 0 | Faculty-wide |
| Major Classification | 3 | Fundamental Subjects (Other Than Introductory Subjects, Subjects of Language Communication) | |
| Minor Classification | 01 | Subjects of Data Science - Data Science 1 | |
| Subject Type | 3 | Elective subject | |
| Supplemental Course Information | Class Classification | 2 | Lecture |
| Class Format | 1 | Face-to-face classes (conducted mainly in-person) | |
| Language of Instruction | 1 | Japanese | |
| Academic Discipline | 12 | Analysis, applied mathematics, and related fields | |
Course Summary
This is an introduction to the mathematical theory of probability. We begin with the basics of set theory, mathematical logic, and combinatorics, on which we build probability theory. After introducing the concept of probability, we cover fundamental topics in probability theory: conditional probability, independence, Bayes' theorem, random variables, probability distributions, expectation, variance, and the central limit theorem.
Course Description/Objectives/Teaching Method/Intended Learning Outcome
The theme of this lecture is the mathematical theory of probability with a focus on data science. Probability is, in fact, a fundamental tool in statistics, information theory, and computer science. Building on high school mathematics, we will explore several important topics in probability. The goal is to develop familiarity with this increasingly important subject so that students can freely apply basic probability theory in their respective fields of study in the future.
Course Taught by Faculty Member with Professional Experience
Not applicable
Active Learning MethodsDescription
Not applicable
Preparatory Study
Follow the teacher's instructions and solve problems related to the content covered in class (focusing on review for approximately four hours).
Course Plan
Lesson 1
Title
Introduction, Set Theory
Overview
Overview, Set theory
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 2
Title
Number of cases
Overview
Permutations, Combinations
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 3
Title
Basics of Probability
Overview
Events, Sample spaces, Empirical probability, Probability law
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 4
Title
Conditional Probability
Overview
Joint probability, Conditional probability, Independency
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 5
Title
Bayes' theorem
Overview
Bayes' theorem, Time-reversing, Monty Hall problem
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 6
Title
Random Variables
Overview
Random variables, Distributions, Expectation values, Marginal probability
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 7
Title
Expected Value, Variance, Standard Deviation
Overview
Expected value, Variance, Standard deviation
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 8
Title
Mean, Median, Mode, Probability Inequality
Overview
Mean, Median, Mode, Simpson's paradox, Chebyshev's inequality, Markov's inequality
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 9
Title
Several Random Variables
Overview
Covariance, Correlation coefficient, Causation, Spurious relationship
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 10
Title
Discrete Probability Distributions
Overview
Discrete probability distributions, Bernoulli, Binomial, Geometric, Poisson
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 11
Title
Cumulative Distribution Function, Probability Density Function
Overview
Cumulative distribution function, Probability density function
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 12
Title
Continuous Probability Distribution
Overview
Continuous probability distribution, Uniform, Exponential, Normal, Standard normal distribution table
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 13
Title
Advanced topics
Overview
Law of large numbers, Central limit theorem
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Lesson 14
Title
Summary of Class
Overview
Wrap-up of this class
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Other
Title
Final Examination
Overview
Final examination
Faculty Member/Instructor in Charge
Shotaro Sakai
Class Format
Same as the whole Class Format
Method of Evaluation
Evaluation will be based on attendance, assignments for the lecture, and an exam.
Generative AI Policy for Classes
In this course, in order to emphasize students' own thinking skills, the use of generative AI in the preparation of reports is prohibited. However, the use of such tools for the purpose of deepening understanding is not discouraged, provided that students verify the accuracy of any information obtained.
Textbooks
No specific designation.
Reference Books
Lecture materials will be made available for download from K-LMS.
Lecturer's Comments to Students
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