For three categorical variables X, Y, and Z: a. Prove that mutual independence of X, Y, and
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For three categorical variables X, Y, and Z:
a. Prove that mutual independence of X, Y, and Z implies that X and Y are both marginally and conditionally independent.
b. When X is independent of Y and Y is independent of Z, does it follow that X is independent of Z? Explain.
c. When any pair of variables is conditionally independent, explain why there is no three-factor interaction.
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