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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. f (x) Sometimes we're simultaneously interested in two or more variables in a random experiment.

Mean from a Joint Distribution If Xand Y are continuous random variables with joint probability density function fXY(x;y), then E(X) = Z 1 1 xfX(x) dx = Z 1 1 Z 1 1 xfXY(x;y) dydx HINT: E(X) and V(X) can be obtained by rst calculating the marginal probability distribution of X, or fX(x). 22

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Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 1 ...

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