Transcription of Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 1 ...
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Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 1 ...
Chapter 5: JOINT PROBABILITY . DISTRIBUTIONS . Part 1: Sections to For both discrete and continuous random variables we will discuss the JOINT DISTRIBUTIONS (for two or more 's). Marginal DISTRIBUTIONS (computed from a JOINT distribution ). Conditional DISTRIBUTIONS ( P (Y = y|X = x)). Independence for 's X and Y. This is a good time to refresh your memory on double-integration. We will be using this skill in the upcom- ing lectures. 1. Recall a discrete PROBABILITY distribution (or pmf ) for a single X with the example be- x 0 1 2.
Given random variables Xand Y with joint probability fXY(x;y), the conditional probability distribution of Y given X= xis f Yjx(y) = fXY(x;y) fX(x) for fX(x) >0. The conditional probability can be stated as the joint probability over the marginal probability. Note: we can de ne f Xjy(x) in a similar manner if we are interested in that ...
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