Please help me answer the following question dealing with join distributions. Thanks in advance!

(a) Can there exist three random variables X1,X2,X3, each taking values in the set {+1, 1}, with the property that for every 1' 7E j, the joint distribution of X; and X J- is given by 1 1 PlXi=1an=1l= IP[)(j=1,Xj=1]= PiXiszl=0? (1) If so, specify the joint distribution of X1,X2,X3; if not, prove it. (b) For which natural numbers n 2 3 can there exist random variables X1,X2, ...,Xn, each taking values in the set {+1, 1}, with the property that for every 1' and j satisfying i j = 1 (mod n), the joint distribution of X; and X j is given by (1)? For any n that work, specify the joint distribution; for those that do not, prove it