Consider five random variables U, V, W, X, and Y whose joint distribution satisfies: P(U, V, W, X, Y) = P(U)P(V)P(W U, V)P(X W)P(Y W) Which ONE of the following statements is FALSE?

U and V are conditionally independent given W

Y is conditionally independent of V given W

X is conditionally independent of U given W

U and V are conditionally independent given W

Y and X are conditionally independent given W

GATE DA 2024 Q24: False conditional independence in a factorised distribution

Consider five random variables $U, V, W, X$ , and $Y$ whose joint distribution satisfies:

$P(U, V, W, X, Y) = P(U)P(V)P(W \mid U, V)P(X \mid W)P(Y \mid W)$

Which ONE of the following statements is FALSE?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: C (official GATE 2024 final answer key)

Concept used: d-separation in Bayesian networks; observing a common child (collider) makes its parents dependent.

First step: The network is $U \to W \leftarrow V$ , $W \to X$ , $W \to Y$ ; $W$ is a collider for $U$ and $V$ .

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key