8.3 ( ) Consider three binary variables

a, b, c ∈ {0, 1} having the joint distribution given in Table 8.2. Show by direct evaluation that this distribution has the property that a and b are marginally dependent, so that p

(a,

b) = p(a)p(b), but that they become independent when conditioned on

c, so that p

(a, b|c) = p(a|c)p(b|c) for both c = 0 and c = 1.