Consider five random variables π‘ˆ, 𝑉, π‘Š, 𝑋, and π‘Œ whose joint distribution…

Consider five random variables π‘ˆ, 𝑉, π‘Š, 𝑋, and π‘Œ whose joint distribution satisfies:

𝑃(π‘ˆ, 𝑉, π‘Š, 𝑋, π‘Œ) = 𝑃(π‘ˆ)𝑃(𝑉)𝑃(π‘Š|π‘ˆ, 𝑉)𝑃(𝑋|π‘Š)𝑃(π‘Œ|π‘Š)

Which ONE of the following statements is FALSE?

  1. A.

    π‘Œ is conditionally independent of 𝑉 given π‘Š

  2. B.

    𝑋 is conditionally independent of π‘ˆ given π‘Š

  3. C.

    π‘ˆ and 𝑉 are conditionally independent given π‘Š

  4. D.

    π‘Œ and 𝑋 are conditionally independent given π‘Š

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