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Monthly Archives: June 2019

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30Jun 2019

MIT RES.6-012 Introduction to Probability 5강

by jacob

L05.2 Definition of Random Variables
https://youtu.be/vfqPpai_9jI

random variable 개념 잡기 참고 영상

https://youtu.be/3v9w79NhsfI

실제 상황에서 동전을 던진 경우 head, tail이 나올수 있는데 이 각각의 경우를 1, 0으로 대응 시켜 주는 함수가 random variable이다. 주사위를 던져서 나온 값들의 합이렇게 기술하는 것보다 이에 대응하는 값을 만들어 주는 random variable Y를 이용하는 것이 더 깔끔한 것을 알수 있다.

L05.3 Probability Mass Functions
https://youtu.be/zW1_iugJvF0

L05.4 Bernoulli & Indicator Random Variables
https://youtu.be/J8L9kRGSvSY

L05.5 Uniform Random Variables
https://youtu.be/JoQDJMZA7F8

L05.6 Binomial Random Variables
https://youtu.be/jOC4ATKBWlI

L05.7 Geometric Random Variables
https://youtu.be/whbKmwMmB4s

L05.8 Expectation
https://youtu.be/_yJsO5955ZE

indicator function에 대하여

https://youtu.be/V3pnr5gmJC8

L05.9 Elementary Properties of Expectation
https://youtu.be/GARQ31BrKQA

L05.10 The Expected Value Rule
https://youtu.be/gB5TCCfF6e4

L05.11 Linearity of Expectations
https://youtu.be/0IJFBMIU6x4

맨 하단의 파란색으로 써있는 내용은 오직 linear 연산에만 적용된다.

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30Jun 2019

MIT RES.6-012 Introduction to Probability 3강

by jacob ⋅ Link

L03.2 A Coin Tossing Example
https://youtu.be/rZKUmNvCjis

위 그림에서 P(H2) 는 첫번째 어느 것을 선택하든 상관없이 두번째에 head가 나오는 경우를 말한다. 그러므로 첫번째 tail, head나온 경우의 경우수를 합해준다.

P(H2 | H1) 의 경우는 첫번째에는 head가 나오고 그 다음에 두번째에 head가 나온 경우를 말한다.

L03.3 Independence of Two Events
https://youtu.be/w423ypsUHf0

disjoint는 independent가 아니다.

L03.4 Independence of Event Complements
https://youtu.be/JZkT3NU2mPM

A 와 B가 independent이면 A 와 B complement도 independent이다.

L03.5 Conditional Independence
https://youtu.be/7B3cDe39lwY

L03.7 Independence of a Collection of Events
https://youtu.be/UbQcqFH33G0

내 추측:

A1과 A2, A1과 A3, A2와 A3가 pairwise independence라고 하더라도 A1, A2, A3가 다같이 indepedent하다고 할수 없다. 다음 그림을 보고 확인할것. 위의 그림에서 맨밑 빨간글씨는 오해를 불러 일으키는 것 같다.

L03.8 Independence Versus Pairwise Independence
https://youtu.be/aJXfyfQs2Mc

pairwise independent라고 해서 independent라는 이야기는 아니다.

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29Jun 2019

MIT RES.6-012 Introduction to Probability 2강

by jacob ⋅ Link

L02.2 Conditional Probabilities
https://youtu.be/MPRKc4UPoJk

L02.3 A Die Roll Example
https://youtu.be/YenDB3yOfDc

Conditional Probabilities의 예시

L02.4 Conditional Probabilities Obey the Same Axioms
https://youtu.be/L_pEeYLGaP0

L02.5 A Radar Example and Three Basic Tools
https://youtu.be/uL31gpFdarc

L02.6 The Multiplication Rule
https://youtu.be/ugzs7dgQ-JE

L02.7 Total Probability Theorem
https://youtu.be/8odFouBR2wE

L02.8 Bayes’ Rule
https://youtu.be/kz2tvO_ZAKI

밑의 공식의 밑변은 Total Probability Theorem에서 나온것이다. 윗 부분은 conditional probability에서 유도된것이다.

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29Jun 2019

MIT RES.6-012 Introduction to Probability 1강

by jacob

L01.4 Probability Axioms
https://youtu.be/pA83XtLeVig

L01.5 Simple Properties of Probabilities
https://youtu.be/WTyLg_I1oFY

L01.6 More Properties of Probabilities
https://youtu.be/N3I2ZLbh6zQ

L01.7 A Discrete Example
https://youtu.be/AsSQdpZdP8U

P(X=1)이라고 하면 random variable (확률변수) X가 1의 값을 가지는 확률값을 말한다.

discrete uniform law는 sample space에서 각각의 element가 같은 발생 확률을 가진다는 것을 설명한다.

L01.8 A Continuous Example
https://youtu.be/NbYB0fiHoCs

L01.9 Countable Additivity
https://youtu.be/mUxg3j_h5GM

L01.10 Interpretations & Uses of Probabilities
https://youtu.be/uGGTX2ypzKI

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29Jun 2019

MIT RES.6-012 Introduction to Probability 1강

by jacob ⋅ Link

L01.4 Probability Axioms
https://youtu.be/pA83XtLeVig

L01.5 Simple Properties of Probabilities
https://youtu.be/WTyLg_I1oFY

L01.6 More Properties of Probabilities
https://youtu.be/N3I2ZLbh6zQ

L01.7 A Discrete Example
https://youtu.be/AsSQdpZdP8U

P(X=1)이라고 하면 random variable (확률변수) X가 1의 값을 가지는 확률값을 말한다.

discrete uniform law는 sample space에서 각각의 element가 같은 발생 확률을 가진다는 것을 설명한다.

L01.8 A Continuous Example
https://youtu.be/NbYB0fiHoCs

L01.9 Countable Additivity
https://youtu.be/mUxg3j_h5GM

L01.10 Interpretations & Uses of Probabilities
https://youtu.be/uGGTX2ypzKI

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27Jun 2019

통계학 한국어 channels

by jacob ⋅ Link

https://www.youtube.com/channel/UCJ2-Cr7HV5s5dE2Qx-CaQVA/playlists

https://www.youtube.com/user/who4u78/playlists

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27Jun 2019

MIT RES.6-012 Introduction to Probability 12강

by jacob ⋅ Link

L12.6 Covariance Properties

https://youtu.be/RQKJBpaCCeo

L12.7 The Variance of the Sum of Random Variables

https://youtu.be/GH7dwoXSD0s

L12.8 The Correlation Coefficient

https://youtu.be/HTs6Zhc2S1M

L12.9 Proof of Key Properties of the Correlation Coefficient

https://youtu.be/uxVRfj60z98

L12.10 Interpreting the Correlation Coefficient

https://youtu.be/J3aMHIajtFc

위의 예식에서는 correlation값이 1/2이 나왔다 . correlation 값이 0인 경우 두 random variables이 관계가 없다. independent하다고 할수 있다.

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