Question

This problem investigates the wa in which conditional independence relationships affect the amount of in formation needed for probabilistic calculations. (a) Suppose we wish to calculate p(AB-1,C-1), and we have no conditional independence information. Which of the following sets of numbers are sufficient for the calculation? (1) p(B,C), p(A), p(B|A), p(CA) (2) p(B,C), p(A), p(B, C1A) (3) p(A), p(BIA), p(C|A) b) Now suppose that we also know that p(BIA, C)-p(BA) for all values of A, B, C. Now which of the three sets are sufficient?

Answer 1

AnSwe Given B A e ะ Fnon® klekove to find plAnBne) but none of hom (1) We have To ndt SuHfiCedt Calte Ple.cla) pía) PIB,CIA). PIA) pia) lBnc) Pl Bnc)

ie To Calculale => none of this each give plAnBnc) in "Nome"ato" So Ihese ai not Soff.Cient ple.cl, pla), ple iA), pícla) 8,c) (0 nc) piana) Plenc) BnAnc) PlBnc)

So if Pela) pIBlAc) then Jiven injomation ple.c), Pla), ple.cla) Sotficieat Pia), PlBlA) plela) on uSi hese bie Can not bi plBnc) in enominaloi an hou So thene not Sofficient