The next series of questions concern the following Bayesian Network from Santos et al$.$:

Santos, E$.,$ & Shimony, S$.$ E$.(1998).$ Deterministic approximation of marginal probabilities in bayes nets. IEEE Transactions on

Systems, Man, and Cybemetics$-$Part A: Systems and Humans, $28(4),377-393.$

You may use abbreviations for your solutions, but you must define them in a key in Q$1.$

For examples: Let $SC=$ severe cough, $HC=$ heart condition....

Write the global distribution for the Bayesian Network in factored form.

Identify all of the v$-$structures in the graph $($you may draw them or write them$).$

Is Allergy independent of Bronchitis? $($yes or no$)$

$($Allergy ${?}_{|}{?}_{?}$ Bronchitis$)$

Is Allergy independent of Bronchitis given information about Sneezing? $($yes or no$)$

$($Allergy ${?}_{|}{?}_{?}$ Bronchitis $|$ Sneezing$)$

Suppose every node in the Medical Diagnosis BN is discrete and has two possible states.

What are the dimensions of the Conditional probability tables for the following:

a$)$ High temperature

b$)$ Severe cough

c$)$ High blood pressure

Draw the moral graph for the Medical Diagnosis BN$.$

In the Medical Diagnosis BN: