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.
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
|Intercultural skills||Communication skills||✔ Specialist skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
Each class starts with the 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|
|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||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 a random number (linear congruent method, Box-Muller’s method|
|Class 10||law of great numbers||Understanding a law of great numbers (Independent and identically distributed, a law of great numbers, central limit theorem)|
|Class 11||Statistical inference||Understanding statistical inference (point estimation, moment method, maximum-likelihood method)|
|Class 12||Hypothesis testing||Understanding hypothesis testing (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|
Students' knowledge and their ability will be assessed mainly by a midterm report and final examination. The weight of the midterm report is equal to that of the final examination.