Question

Problem 2 Consider the following Bayesian network for detecting credit-card fraud: pla <30)-0.25 pla-30-50)-0.40 ps-male)-o.s p(-yes)-0.00001 Fraud Age Sex Jewelry pig yeslf-yes)-0.2 pig yeslf-no)-0.01 pU yeslf-no,a 30,s-male)-0.0001 PV=yesV-no,a-30-50.5-male)-0.0004 PV "yes f-no,a =>50.5-male) = 0.0002 pf yesfeno,a 30,s female)-0.0005 PU =yes ir-no,a-30-50.5-emale) = 0.002 PV=yesy-noa->50.5-female) = 0.001 Arcs (arrows) are drawn from cause to effect, eg., the stolen card used for either gas or jewelry. It means that the current effect is dependent only on its parent node, which represents its cause. The local probability distribution(s) associated with a node are shown adjacent to the node. An asterisk is a shorthand for lany state. Let us use a random vector (F, A, S, G, J) to denote the events of Fraud, Age, Sex, Gas, Jewelry. Note that all these random variables are discrete, e.g., Fraud or not fraud, Used for gas or Not used for gas, Used for jewelry or Not used for jewelry, Used by male or Used by female, Age above 30 or Age below 30 (a) Find the joint probability mass function Prafa.g.s,) in terms of local probability distribution, i.e., conditional probability mass functions. Using the local probability distribution, then, discuss how many possible values of the joint probability mass function arce required for presenting its probability density function, i.e., how many delta functions are required? (b) Compute the conditional probability that the card is stolen when Age 30, Used for Gas and Jewelry, and Used by Male

Answer 1

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