Problem 1 Independence in Bayesian Networks Consider the Bayesian network below. 2 T3 X6 a) (15 pts) Identify if each independence statement is true or false. A statement is true if it is true for any probability distribution that factorizes with respect to the network above, that is, it must follow from d-separation. i) x1 1 x2 23; i) x1, 18 1 24 2 2; iii) 23 1 24 22; iv ) x1 1 x2 x6; v) X8 1 x1 22, 23; b) (10 pts) List all independence properties of the form x; I x; that follow from d-separation. Note that there is no conditioning