Basics of Multivariate Probability

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Presentation transcript:

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

Probability w.r.t Process with Uncertain Outcome

Example

Interpretations of Probability

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

Marginal Probability

Conditional Probability

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

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

Conditional Example

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