Time: Mon3 13:00-14:30

Class Room: Zoom

Lecturer: Atsushi Kanazawa 

[Contact]

atsushik(at mark)sfc.keio.ac.jp

[Description]

This is an introduction to the mathematical theory of probability. We begin with basics of set theory, combinatorics, based on which we develop probability theory. After introducing the concept of probability, we cover basic topics such as conditional probability, independency, Bayes' theorem, random variables, probability distributions, expectation, variation, law of large numbers, central limit theorem. The goal of the lecture is to become accustomed to this increasingly important subject so that in the future students will be free to apply basic theory in their field of study.

[Assignments, Examination & Grade Evaluation]

Final Exam (40%) + Reports (60%)

There will be 3 reports (20 points each). 

[Materials & Reading List]

Lecture notes and slide will be uploaded on SOL. 

Lectures are recorded and shared on SOL for reviews. 

[Schedule]

10/4 1st Lecture: introduction, set theory (slide)

10/11 2nd Lecture: set operations, Russell's paradox, prior probability (slide)

10/18 3rd Lecture: empirical probability, probability law, joint probability, addition rule, independency (slide)

10/25 4th Lecture:  conditional probability, independency (revised), Bayes' theorem (slide)

11/1 5th Lecture: Bayes' theorem (continued), classical problems  (birthday, Monty Hall, prosecutor's fallacy, boy and girl) (slide)

11/8 6th Lecture: random variables, distributions, expectation values (slide)

11/15 7th Lecture:  expectation values, variance, standard deviation (slide)

11/22 (三田祭, Mita Festival)

11/29 8th Lecture: mean, median, mode, Simpson's paradox, Chebyshev's inequality, Markov's inequality (slide)

12/6 9th Lecture: covariance, correlation coefficient, causation, spurious relationship (slide)

12/13 10th Lecture: discrete probability distributions (Bernoulli, binomial, Poisson, geometric, etc), Poisson approximation (slide)

12/20 11th Lecture: continuous probability distribution, cumulative distribution function, probability density function (slide)

1/7(Substitute Monday) 12th Lecture: normal distribution, law of large numbers, central limit theorem (slide)

1/10 (成人の日, Coming of Age Day)

1/17 13th Lecture: review, mock final exam (slide)

1/24 14th lecture: online final exam (open-book style)