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Thanks for your support with the following questions! Conditional Independence 2 Suppose three random variablesX ,Y ,Z have a joint distribution P X,Y,Z (x,y,z)=P X(x)

Thanks for your support with the following questions!

Conditional Independence 2

  1. Suppose three random variablesX ,Y ,Z have a joint distribution P X,Y,Z (x,y,z)=P X(x) PZX (zx)P YZ (yz).

Then,XandY are independent givenZ ?

  1. Suppose random variablesXandYare independent givenZ, then the joint distribution must be of the formPX,Y,Z(x,y,z)=h(x,z)g(y,z), whereh,g are some functions.
  2. True or false?

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