Full conditionals:
Let X, Y, Z be random variables with joint density (discrete or continuous) p(x, y, z) ? f(x, z)g(y, z)h(z). Show that
a) p(x|y, z) ? f(x, z), i.e. p(x|y, z) is a function of x and z;
b) p(y|x, z) ? g(y, z), i.e. p(y|x, z) is a function of y and z;
c) X and Y are conditionally independent given Z.