Mathematics, 07.03.2020 04:42, Morganwing1019

Let X, Y, Z be random variables. Prove or disprove the following statements. (That means, you need to either write down a formal proof, or give a counterexample.)

Statement 1. If X and Y are (unconditionally) independent, is it true that X and Y are conditionally independent given Z?

Statement 2. If X and Y are conditionally independent given Z, is it true that X and Y are (unconditionally) independent?

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Let X, Y, Z be random variables. Prove or disprove the following statements. (That means, you need t...