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.

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

https://youtu.be/mUxg3j_h5GM

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

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.

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