Full conditionals: Let X, Y , Z be random variables with joint density (disrete 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 .

I DON'T REALLY EVEN KNOW HOW TO START THIS PROBLEM. PLEASE HELP!

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 .

I DON'T REALLY EVEN KNOW HOW TO START THIS PROBLEM. PLEASE HELP!

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