기초 확률론

확률 변수와 확률 과정 (Random Variable and Random Process)

담당 교수

서울대학교 전기정보공학부 심형보

강의 언어

한국어

강의 소개

확률을 처음 접하는 사람들을 위한 과목으로, 확률의 정의부터 시작해서 random variable과 random process를 소개한다. 주어진 확률분포를 갖는 random number를 컴퓨터에서 생성하는 법, entropy의 개념, 확률 변수의 수렴성 정의 등 확률 분야의 기초 지식이 필요한 사람들을 위한 강의이다.

교재

Alberto Leon-Garcia, Probability, Statistics, and Random Processes for Electrical Engineering, Prentice Hall, 2008 (ISBN-10 : 0131471228, ISBN-13 : 978-0131471221)

동영상

Probability model

1강. Probability model, Sample space, Event class, Probability function, Axiom of probability, Borel field, Countably infinite vs uncountably infinite
https://www.youtube.com/watch?v=rIVkvnnDSo4

2강. Computing probability by counting, Conditional probability, Partition of sample space, Bayes' rule
https://www.youtube.com/watch?v=Ls5aqw7k5w8

3강. Independence of events, Sequential experiments, Binomial model, Multinomial model, Geometric model, Markov chain, Pseudo random number generation
https://www.youtube.com/watch?v=LLF6oBBGIfs

Discrete RV

4강. Discrete random variable (RV), Probability mass function (PMF), Expectation, Bernoulli RV, Binomial RV, Geometric RV, MATLAB stem plot
https://www.youtube.com/watch?v=RbSVWHbu7c0

5강. Expectation of functions of RV, Variance, MATLAB computation of expectation for binomial RV
https://www.youtube.com/watch?v=w8nXVk0rzKI

6강. Conditional probability mass function (PMF), Expectation, Variance, Poisson RV
https://www.youtube.com/watch?v=qD4EFFSYYec

Continuous RV

7강. Cumulative distribution function (CDF), Probability density function (PDF)
https://www.youtube.com/watch?v=n8K9QJVY_4Q

8강. Variance, Conditional CDF/PDF, Important RV (uniform, exponential, Gamma, Gaussian), Generation of RV
https://www.youtube.com/watch?v=ZMSuPBOOT7Y

9강. MATLAB code study for exponential RV
https://www.youtube.com/watch?v=BTQ6FqVf6iM

10강. Generation of RV for given PDF, PDF of a function of RV, Markov & Chebyshev inequality
https://www.youtube.com/watch?v=UI1RMiAJ-yA

11강. Characteristic function, Entropy
https://www.youtube.com/watch?v=FeYEITE6JJk

Vector RV

12강. Joint pmf/cdf/pdf (of X and Y), Marginal pmf/cdf/pdf, Independent RV, Correlation, Covariance, Correlation coefficient, Joint Gaussian RV
https://www.youtube.com/watch?v=sRjGkR9ybew

13강. Conditional probability, Conditional expectation, Vector RV
https://www.youtube.com/watch?v=3vZVrT9lP_k

14강. Functions of several RV
https://www.youtube.com/watch?v=1JNsCY02QyY

15강. Expectation (of vector RV), Diagonalization of a matrix, Joint Gaussian vector RV, Generating joint Gaussian RV
https://www.youtube.com/watch?v=CXwYlOfNSww

16강. Estimation
https://www.youtube.com/watch?v=MQRheH5YShc

Sum of RV

17강. Law of large numbers, Convergence of sequence of RV
https://www.youtube.com/watch?v=Kjhvx1z3TjM

18강. Review of convergence of sequence of RV, Central limit theorem, Gaussian approximation of binomial probability
https://www.youtube.com/watch?v=tPoZcVAVJF8

Random process

19강. Random process (RP), Auto-correlation, Auto-covariance
https://www.youtube.com/watch?v=vK7RjVR_Pl0

20강. Important RP (Sum RP, Poisson RP), Incremental independence, Incremental stationary
https://www.youtube.com/watch?v=PXxzc92MMaw

21강. Gaussian RP, Wiener RP, (Strict-, Wide-)sense stationary RP
https://www.youtube.com/watch?v=nPApzzftm5I

22강. Properties of WSS, Mean square continuity/differentiability
https://www.youtube.com/watch?v=qRA3yDTisB0

23강. Propagation of random signal through linear system, Ergodicity
https://www.youtube.com/watch?v=_k7qzox6KWQ

24강. Power spectral density (PSD), Propagation of PSD through linear system
https://www.youtube.com/watch?v=WS3EeBM05go

Statistics

25강. Sample mean, sample variance, Maximum likelihood estimator (MLE)
https://www.youtube.com/watch?v=ELVGlAek_-I

26강. Cramer–Rao inequality, Fisher information, Properties of MLE
https://www.youtube.com/watch?v=-QcxDHbZE80

27강. Confidence interval, Significance testing, Null hypothesis
https://www.youtube.com/watch?v=Bf-3StSEbik

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