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 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
|✔ Specialist skills||Intercultural skills||Communication 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, 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)|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
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 two that of the final examination.