Probability & Statistics Notes

I just finished the probability and statistics courses. I used the online Khan academy courses. These courses are excellent. Teachers there can guide you from basics to advanced topics step by step. I think it's a good place for self-study. Probability and statistics courses are the most difficult ones for me to crack down mathematical fundamentals required for machine learning.I spent almost more than two weeks to get familiar with these terms and formulas. Basically, probability deals with the occurring rates of certain events in a given event space (they call it sample space),and properties of these rates associated with our beliefs.Statistics concerns itself with how to find laws behind certain sets of samples, and use these laws to guide human activities. For machine learning, the most important parts of the two courses include:

1, Bayes rule

2, The product rule

3, Mean value theorem

4, Variance

5, Covariance

6, Joint distribution

7, Independent distribution

8, probability mass function

9, probability density function

10, margin probability

11, Markov chain

These parts would help me better understand machine learning concepts.