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

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

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Conditional Probabilities의 예시

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

L12.6 Covariance Properties

https://youtu.be/RQKJBpaCCeo

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L12.7 The Variance of the Sum of Random Variables

https://youtu.be/GH7dwoXSD0s

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L12.8 The Correlation Coefficient

https://youtu.be/HTs6Zhc2S1M

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L12.9 Proof of Key Properties of the Correlation Coefficient

https://youtu.be/uxVRfj60z98

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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. 

Covariance (COV: 공분산)란?

19 MOOCs on Mathematics & Statistics for Data Science & Machine Learning