(Solved): 4. Factor marginalization. Let \( X, Z \) be binary variables, and let \( Y \) be a variable that ...

4. Factor marginalization. Let \( X, Z \) be binary variables, and let \( Y \) be a variable that takes on values 1,2 , or 3 . If \( \phi(X, Y, Z) \) is the factor shown below, compute the entries of the factor \[ \psi(Y, Z)=\sum_{X} \phi(X, Y, Z) \] giving your answer according to the ordering of assignments to variables as shown below. Separate the 4 entries of the factor with spaces, and do not add any extra trailing or leading zeroes or decimal points.