HOMEWORK  (Bayesian networks)

Q-1: Answer each of the following questions:
  1. What is the relationship between Bayesian networks and full joint probability distributions?

  2. What is a conditional probability table (CPT)?

  3. What is the Markov blanket of a node in a Baysesian network?

  4. Is there a unique Bayesian network representation for a given full joint probability distribution?

  5. Why does the CPT for a Boolean variable with one Boolean parent contains just two numbers (see the burglary example and CPT for MaryCalls)?

Given the following full joint distribution,

and the following Bayesian network in which the variables Toothache and Catch are conditionally independent given Cavity.
Bayesian network

Complete the Bayesian netowork by giving the CPT for each of the nodes.

Q-3: Consider the following Bayesian network:

Bayesian netowrk Burglary
Compute the following:

  1. P(Burglary), P(Earthquake), P(Burglary=true /\ Earthquake = false)

  2. P(Burglary | Alarm = true), P(Earthquake | Alarm = true), P(Burglary=true /\ Earthquake = false | Alarm = true)