Exercise 13.21 [pv-xyz-exercise]

Show that the statement of conditional independence ${\textbf{P}}(X,Y Z) = {\textbf{P}}(XZ) {\textbf{P}}(YZ)$ is equivalent to each of the statements ${\textbf{P}}(XY,Z) = {\textbf{P}}(XZ) \quad\mbox{and}\quad {\textbf{P}}(YX,Z) = {\textbf{P}}(YZ)\ .$