Let X be any random variable (i.e., node of the Bayes net); let U = {U1, ..., Uk} be the children of X; let V = {V1, ..., Vm} be all of the nodes in X's Markov blanket other than those in U; and let Z = {Z1, ..., Zn} be all of the remaining nodes. Using the definition of conditional probability, marginalization and R&N Eq. (14.1), derive an exact expression for P(X | U, V, Z), the probability of X given all of the other variables, in terms of conditional probabilities of the form P(Y | parents(Y)). Now make a similar computation for P(X | U, V), the probability of X given its Markov blanket. Finally, show that the two expressions that you derived are equal to each other.