Probability

1. Suppose three random variables X , Y , Z have a joint distribution
PX,Y,Z(x,y,z)=PX(x)PZ∣X(z∣x)PY∣Z(y∣z).
Then, are X and Y independent given Z?

2.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)

  1. 👍
  2. 👎
  3. 👁
  1. 1. No
    2. True

    1. 👍
    2. 👎

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