2017 Probability Theory and Statistics

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Academic unit or major
Undergraduate major in Computer Science
Ishida Takashi  Terano Takao 
Course component(s)
Day/Period(Room No.)
Mon1-2(W611)  Thr1-2(W611)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course provides basic probabilistic theory and statistics. The aim of the course is learning the theorem and methods of statistics used in the field of information engineering. Students also learn how to use R-language that 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 test, and use statistical tests properly.


Conditional probability, expected value, variance, binominal distribution, normal distribution, Chebyshev's inequality, hypothesis 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 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
Class 4 Probability distribution Understanding probability and probability distribution
Class 5 Moment Understanding moment (moment, moment-generating function)
Class 6 probability inequality Understanding probability inequality (Chebyshev's inequality)
Class 7 Discrete probability distribution Understanding discrete probability distribution (binominal distribution, Bernoulli distribution, Poisson distribution)
Class 8 Continuous probability distribution Understanding continuous probability distribution (normal distribution, exponential distribution)
Class 9 Random number generation Understanding how to generate random number (linear congruent method, Box-Muller’s method
Class 10 law of great numbers Understanding law of great numbers (Independent and identically distributed, law of great numbers, central limit theorem)
Class 11 Statistical inference Understanding statistical inference (point estimation, moment method, maximum-likelihood method)
Class 12 Hypothesis test Understanding hypothesis test (significance level, type I/II error)
Class 13 t-test Understanding t-test (Student’s t-test, Welch’s t-test)
Class 14 Chi-squared test Understanding chi-squared test (F-test, chi-squared test)
Class 15 Statistic-test by R Understanding how to perform statistic-test by R



Reference books, course materials, etc.


Assessment criteria and methods

Students' knowledge and their ability will be assessed mainly by midterm report and final examination. The weight for the midterm report is equal to 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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