Lecture 4: Joint probability distributions; …

Lecture 4: Joint probability distributions; covariance ; correlation10 October 2007In this Lecture we ll learn the following:1. what Joint probability distributions are;2. visualizing multiple variables/ Joint probability distributions; 3. marginalization;4. what covariariance and correlation are;5. a bit more about Joint probability distributionsRecall that a basic probability distribution is defined overa random variable,and a random variable maps from the sample space to the real numbers (R).What about when you are interested in the outcome of an event that is notnaturally characterizable as a single real-valued number,such as the twoformants of a vowel?The answer is really quite simple: probability distributions can be gener-alized over multiple random variables at once, in which casethey are calledjoint probability distributions(jpd s).

Lecture 4: Joint probability distributions; covariance; correlation 10 October 2007 In this lecture we’ll learn the following: 1. what joint probability distributions are;

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