Course title
Probability and Statistics
Course description
We conduct in-person (face-to-face) classes in Spring 2022. Those who are based abroad and who wish take the classes online should contact the lecturer via email.
This course introduces basic concepts of probability and statistics through discussions on the theory and applications. The students will learn fundamental notions of probability such as conditional probability, independence, probability distributions, random variables, expectation, law of large numbers, as well as useful statistical methods such as bootstrapping, maximum likelihood estimators, confidence intervals, and hypotheses testing.
Purpose of class
This class is intended to equip students with basic knowledge and skills of probability and statistics used in science and engineering fields.
Goals and objectives

Goals and objectives Course Outcomes
1. Students will be able to learn fundamental notions of probability such as probability distributions, conditional probability, law of large numbers.
A-1
2. Students will be able to compute probability of events, expectation, variance, covariance, and correlations involving discrete and continuous random variables.
A-1
3. Students will be able to use bootstrapping, maximum likelihood, and least square estimators.
A-1
4. Students will be able to learn exploratory data analysis, sample-size selection for statistical inference, and methods of hypothesis testing as well as their limitations.
A-1
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Discussion on applications of probability and statistics; Outcomes, events, and probability Review Chapters 1 and 2 in the textbook 190分
2. Independence; Conditional probability; Bayes’ rule Review Chapter 3 in the textbook (Homework assignment) 190分
3. Discrete random variables; Probability distributions; Probability mass functions; Discrete-uniform,
binomial distributions
Review Chapter 4 in the textbook 190分
4. Continuous random variables; Cumulative distribution and probability density functions; Uniform,
exponential, pareto, and normal distributions
Review Chapter 5 in the textbook (Homework assignment) 190分
5. Expectation and variance; Simulation and computation with random variables Review Chapter 7, Sections 6.2, 8.1, 8.2 in the textbook 190分
6. Joint distributions; Covariance and correlation Review Chapters 9 and 10 in the textbook (Homework assignment) 190分
7. Law of large numbers, central limit theorem, and some of their applications Review Sections 13.1-13.3, 14.1, 14.2 in the textbook 190分
8. Exploratory data analysis; Sampling; empirical distribution; Basic statistical models Review Sections 15.3, 16.1-16.4, 17.1-17.4 in the textbook (Homework assignment) 190分
9. Bootstrap methods; Estimates and estimators Review Sections 18.1, 18.2, Chapter 19 in the textbook 190分
10. Maximum likelihood and least square estimators Review Chapters 21 and 22 in the textbook (Homework assignment) 190分
11. Confidence intervals; Choice of sample size Review Chapter 24 in the textbook 190分
12. Hypotheses testing; P-Values; Type I and Type II errors; t-test Review Sections 25.1-25.3, 27.1,27.2 (Homework assignment) 190分
13. Discussions on applications of statistical methods Review Sections 28.1-28.4 190分
14. Final exam and discussions on the solutions afterwards Preparation for final 190分
Total. - - 2660分
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Homework Final Total.
1. 15% 15% 30%
2. 15% 5% 20%
3. 15% 5% 20%
4. 15% 15% 30%
Total. 60% 40% -
Evaluation method and criteria
Homework reports will contribute to 60% of the grade; Final exam will contribute to 40% of the grade.
Those who get at least 60% of the full score will pass this course.
Textbooks and reference materials
A Modern Introduction to Probability and Statistics: Understanding Why and How, F. M. Dekking, C. Kraaikamp, H. P. Lopuhaä, L. E. Meester, Springer, 2010.
Prerequisites
The content of Calculus I and Calculus II.
Office hours and How to contact professors for questions
• By appointment. Contact e-mail address: ahmet@shibaura-it.ac.jp
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
• Course that cultivates an ability for utilizing knowledge
• Course that cultivates a basic problem-solving skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals • 4.QUALITY EDUCATION