2022 Probability Theory and Statistics

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Academic unit or major
Undergraduate major in Computer Science
Ishida Takashi 
Class Format
Lecture    (HyFlex)
Media-enhanced courses
Day/Period(Room No.)
Mon1-2(W241)  Thr1-2(W241)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

This course provides basic probabilistic theory and statistics. The aim of the course is to learn the theorem and methods of statistics used in the field of information engineering. Students also learn how to use R-language which is a software environment for statistical computing.

Student learning outcomes

By the end of this course, students will be able to:
1) Understand basic probability theory, and use probability distribution properly.
2) Understand the concept of hypothesis testing, and use statistical tests properly.


Conditional probability, expected value, variance, binomial distribution, normal distribution, Chebyshev's inequality, hypothesis testing, t-test, R-language

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Each class starts with an explanation of a new topic.
In the class occasionally, students are given exercise problems.
Students are asked to submit a midterm report and must take a final examination.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction Understanding descriptive statistics (mean, median, variance)
Class 2 Correlation Understanding correlation (correlation coefficient, liner regression)
Class 3 Introduction to R language Understanding how to process data by R-language
Class 4 Probability distribution Understanding probability and probability distribution
Class 5 Moment, probability inequality Understanding moment (moment, moment-generating function) Understanding probability inequality (Chebyshev's inequality)
Class 6 Discrete probability distribution Understanding discrete probability distribution (binomial distribution, Bernoulli distribution, Poisson distribution)
Class 7 Continuous probability distribution Understanding discrete probability distribution (normal distribution, exponential distribution, gamma distribution, beta distribution)
Class 8 Multi-dimensional probability distributions Understanding Multi-dimensional probability distributions (Multidimensional normal distribution, marginal distribution, convolution)
Class 9 law of great numbers Understanding law of great numbers (Independent and identically distributed, a law of great numbers, central limit theorem)
Class 10 Statistical inference Understanding statistical inference (point estimation, moment method, maximum-likelihood method)
Class 11 Hypothesis testing Understanding hypothesis testing (significance level, type I/II error)
Class 12 t-test Understanding t-test (Student’s t-test, Welch’s t-test)
Class 13 Chi-squared test Understanding chi-squared test (F-test, chi-squared test)
Class 14 Multiple comparison procedure, advanced statical tests Understanding various advanced statical tests (Bonferroni method, familywise error rate, Mann–Whitney U test)

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterward (including assignments) for each class.
They should do so by referring to textbooks and other course material.



Reference books, course materials, etc.


Assessment criteria and methods

Students' knowledge and their ability will be assessed mainly by a midterm report and final examination. The weight of the midterm report is one to one that of the final examination.

Related courses

  • CSC.T272 : Artificial Intelligence
  • CSC.T352 : Pattern Recognition
  • CSC.T353 : Biological Data Analysis

Prerequisites (i.e., required knowledge, skills, courses, etc.)


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