Time: Tue3 13:00-14:30

Class Room: Ω21

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.

[Grade Evaluation]

attendance, reports, final exam

[Materials & Reading List]

Lecture notes and slide will be uploaded on SOL. 

[Schedule]

10/3 1st Lecture: introduction, set theory

10/10 2nd Lecture: set operations, Russell's paradox, prior probability

10/17 3rd Lecture: empirical probability, probability law, joint probability, addition rule, independency

10/24 4th Lecture:  conditional probability, independency (revised), Bayes' theorem

10/31 5th Lecture: Bayes' theorem (continued), classical problems  (birthday, Monty Hall, prosecutor's fallacy, boy and girl)

11/7 6th Lecture: random variables, distributions, expectation values

11/14 7th Lecture:  expectation values, variance, standard deviation

11/21 (三田祭, Mita Festival)

11/28 No lecture

12/5 8th Lecture: mean, median, mode, Simpson's paradox, Chebyshev's inequality, Markov's inequality

12/12 9th Lecture: covariance, correlation coefficient, causation, spurious relationship

12/19 10th Lecture: discrete probability distributions (Bernoulli, binomial, Poisson, geometric, etc), Poisson approximation

12/26 11th Lecture: continuous probability distribution, cumulative distribution function, probability density function

1/9 12th Lecture: normal distribution, law of large numbers, central limit theorem

1/16 13th Lecture: review, mock final exam

1/23 14th Lecture: final exam