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# Bayesian Networks

a)
[1 P] Construct a Bayesian network which represents the conditional independence assumptions of the probability distributions from example 1 and 2.

b)
[2 P] Construct two different Bayesian network which encodes exactly the following conditional independence assumptions

c)
[2 P] A doctor gives a patient a drug dependent on their age and gender. The patient has a probability to recover depending on whether s/he receives the drug, how old s/he is and which gender the patient has. Additionally it is known that age and gender are conditional independent if nothing else is known from the patient.1
(i)
Draw the Bayesian network which describes this situation.
(ii)
How does the factorized probability distribution look like?
(iii)
Write down the formula to compute the probability that a patient recovers given that you know if s/he gets the drug. Write down the formula using only probabilities which are part of the factorized probability distribution.

Next: d-separation Up: MLA_Exercises_2013 Previous: Conditional Independence
Hubner Florian 2014-01-21