(Solution) - The random variable X has probability distribution Pr X 0 -(2025 Original AI-Free Solution)

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The random variable X has probability distribution Pr(X = 0) = 0.3, Pr(X = l) = 0.4, and Pr(X = 2) = 0.3. The random variable Y has probability distribution Pr(Y = 1) = 0.6, Pr(Y = 2) = 0.1, and Pr(Y = 3) = 0.3. Find the distribution of Y conditional on X = 2.
Suppose the above random variables are independent. Find the joint distribution and the requested conditional distribution from the given marginal distributions.