Suppose that X and Y are conditionally independent, given Z, and X and Z are marginally independent.

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Suppose that X and Y are conditionally independent, given Z, and X and Z are marginally independent.

a. Show that X is jointly independent of Y and Z.

b. Show X and Y are marginally independent.

c. Show that if X and Z are conditionally (rather than marginally) independent, then X and Y are still marginally independent.

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