# Question: This exercise investigates the way in which conditional

This exercise investigates the way in which conditional independence relationships affect the amount of information needed for probabilistic calculations.

a. Suppose we wish to calculate P (h│e1, e2) and we have no conditional independence information. Which of the following sets of numbers are sufficient for the calculation?

(i) P (E1, E2), P (H), P (E1│H), P (E2│H)

(ii) P (E1, E2), P (H), P (E1, E2│H)

(iii) P (H), P (E1│H), P (E2│H)

b. Suppose we know that P (E1│H, E2) = P (E1│H) for all values of H, E1, E2. Now which of the three sets are sufficient?

a. Suppose we wish to calculate P (h│e1, e2) and we have no conditional independence information. Which of the following sets of numbers are sufficient for the calculation?

(i) P (E1, E2), P (H), P (E1│H), P (E2│H)

(ii) P (E1, E2), P (H), P (E1, E2│H)

(iii) P (H), P (E1│H), P (E2│H)

b. Suppose we know that P (E1│H, E2) = P (E1│H) for all values of H, E1, E2. Now which of the three sets are sufficient?

**View Solution:**## Answer to relevant Questions

Let X, Y, Z be Boolean random variables. Label the eight entries in the joint distribution P (X. Y, Z) as a through h. Express the statement that X and Y are conditionally independent given Z as a set of equations relating a ...In our analysis of the wumpus world, we used the fact that each square contains a pit with probability 0.2, independently of the contents of the other squares. Suppose instead that exactly N/5 pits are scattered uniformly at ...Investigate the complexity of exact inference in general Bayesian networks:a. Prove that any 3-SAT problem can be reduced to exact inference in a Bayesian network constructed to represent the particular problem and hence ...We outlined a flawed procedure for finding the most likely state sequence, given an observation sequence. The procedure involves finding the most likely state at each time step, using smoothing, and returning the sequence ...Tickets to a lottery cost $1. There are two possible prizes: a $10 payoff with probability 1/50, and a $1,000,000 payoff with probability 1/2,000,000. What is the expected monetary value of a lottery ticket? When (if ever) ...Post your question