a. Suppose A ⊥⊥ B. Determine the missing entries x and y of the joint distribution P(A, B), where A and B take values in {0, 1}. 

P(A = 0, B = 0) = 0.1 

P(A = 0, B = 1) = 0.3 

P(A = 1, B = 0) = x 

P(A = 1, B = 1) = y 

b. Suppose B ⊥⊥ C | A. Determine the missing entries x, y, z of the joint distribution P(A, B, C). 

P(A = 0, B = 0, C = 0) = 0.01 

P(A = 0, B = 0, C = 1) = 0.02 

P(A = 0, B = 1, C = 0) = 0.03 

P(A = 0, B = 1, C = 1) = x 

P(A = 1, B = 0, C = 0) = 0.01 

P(A = 1, B = 0, C = 1) = 0.1 

P(A = 1, B = 1, C = 0) = y 

P(A = 1, B = 1, C = 1) = z