(Solved): Entropy and pairwise independence. \( \quad \) Let \( X, Y, Z \) be three binary Bernouli \( \left ...

Entropy and pairwise independence. \( \quad \) Let \( X, Y, Z \) be three binary Bernouli \( \left(\frac{1}{2}\right) \) random variables that are pairwise independent; that is \( I(X ; Y)=I(Y ; Z)=I(X ; Z)=0 \) (a) Under this constraint, what is the minimum value for \( H(X, Y, Z) \) ? (b) Give an example achieving this minimum.