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If it is known that Bayesian network has one root node, one node with a single parent, two nodes with two parents and the remaining nodes with 3 parents, indicate how many parameters would be required to define this Bayesian network? Do this for the following combination of number of variables (n) and their values (m): a) n = 20 and m = 2; b) n = 20 and m = 5; c) n = 500 and m = 10;

I'm not sure how to answer this question. I know that there's a formula which states that the number of parameters equals to m^n - 1, where n is a number of variables and m is the number of values per variable. Could someone please help me understand this question better?

Thanks!

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I think the question is asking "how many parameters would be required to choose among any probability distribution compatible with this Bayesian network?". Any compatible distribution must be represented as a product of conditional probability tables (CPTs). So the question is asking how many parameters do you need to specify all of the CPTs in the given network (assuming all the CPTs can be different).

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