Consider N variables each taking K values.How many free parameters do we need to model the N variables as a joint probability table?How many free parameters do we need to model the marginal probability of one variable?Note: The number of parameters for all the marginal probabilities will be N times the answer to b). This number is smaller than the answer to a). This gives a hint that marginals are inadequate to define the joint probability.

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Consider N variables each taking K values. How many free parameters do we need to model the N variables as a joint probability table?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Consider N variables each taking K values.

How many free parameters do we need to model the N variables as a joint probability table?
How many free parameters do we need to model the marginal probability of one variable?

Note: The number of parameters for all the marginal probabilities will be N times the answer to b). This number is smaller than the answer to a). This gives a hint that marginals are inadequate to define the joint probability.

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