1. Basics of Multivariate Probability
Recap of Lecture 1
Basics of Multivariate Probability
Mathematical definitions
Interpretation of probability
Multivariate probability

2. Probability w.r.t Process with Uncertain Outcome

3. Example

4. Interpretations of Probability

5. Joint Distribution
Assign a probability value for each combination of values of the random variables
P(R, T) refers to a table. So do P(X, Y, Z), …
Number of free parameters: 3 x 4 – 1 = 11

6. Marginal Probability

7. Conditional Probability

8. (Marginal) Independence
Two-dimensional table reduced to one-dimensional table

9. Conditional Independence
Three-dimensional table reduced to two-dimensional table

10. Conditional Example