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?