Show that x and y are conditionally independent given z

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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.

Reference no: EM131201174

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