**Q1)** The question below encodes a set of independencies among the following variables Income (a), Deposit(B), Housing(E), Payment(C) and Security(D). Answer the following sub questions.

**I) **Indicate whether the following independence statements are true or false according to this model. Provide a very brief justification of your answer (not more than two or three

sentences)

1. Income ⊥ Security

2. Income ⊥ Security | Payment

3. Income ⊥ Payment

4. Income ⊥ Security | Payment, Deposit

5. Deposit ⊥ Payment

6. Income ⊥ Payment | Deposit

**II) **Show the factorized form of the joint distribution over all of the variables, P(A, B, C, D, E)

**III) **Find out probability for payment is false, when no prior information is available.

**IV) **What is the probability that you have got Payment, given that the income is low?

**V)** What is the probability that you have got Payment, given that the income is low and you have large deposits?

**VI) **What is the probability that you didn’t default in payment given high income and no

security is given?

**Q2) **Given the Bayesian network, answer the below mentioned questions.

**I) **Does knowing that you have Lung Cancer increase or decrease your likelihood of having Bronchitis? Intuitively, does this make sense?

**II)** What is the probability that you have the tuberculosis, given that you have visited Asia, you have Lung Cancer, and you know that you have positive x-ray?

**III)** What is the probability of having Dispnea given that you have positive x-ray.

**IV) **Find out all the independencies in the graph.

*To get solution code script of above requirement or any other **Probabilistic Graphical Machine Learning model project** then send your requirement details at:*

realcode4you@gmail.com

## Comments