- 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.