Question: Suppose three random variables X, Y, Z have a joint distribution PX,Y,Z(x,y,z)=PX(x)PZX(zx)PYZ(yz). Then, X and Y are independent given Z.(True or False) Suppose random variables

Suppose three random variables X, Y, Z have a joint distribution

PX,Y,Z(x,y,z)=PX(x)PZX(zx)PYZ(yz).

Then, X and Y are independent given Z.(True or False)

Suppose random variables X and Y are independent given Z, then the joint distribution must be of the form

PX,Y,Z(x,y,z)=h(x,z)g(y,z),

where h,g are some functions.(True or False)

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