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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. We're looking for a relationship between the two variables.

We show the probability for each pair in the following table: x=length 129 130 131 y=width 15 0.12 0.42 0.06 16 0.08 0.28 0.04 The sum of all the probabilities is 1.0. The combination with the highest probabil-ity is (130;15). The combination with the lowest probability is (131;16). The joint probability mass function is the func-

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Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 3: The ...

homepage.stat.uiowa.edu

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Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 1 ...

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Chapter 5: JOINT PROBABILITY DISTRIBUTIONS Part 1: Sections 5.1 & 5.2 For both discreteand continuousrandom variables we will discuss the following... Joint Distributions (for two or more r:v:’s) Marginal Distributions (computed from a joint distribution) Conditional Distributions (e.g. P(Y = yjX= x)) Independence for r:v:’s Xand Y

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homepage.stat.uiowa.edu

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homepage.stat.uiowa.edu

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homepage.stat.uiowa.edu

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