a) Let X, Y, Z be random variables. Letr, y, z be the realized values of...

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a) Let X, Y, Z be random variables. Letr, y, z be the realized values of the random variables X, Y, Z. Use the definitions of conditional probabilities to prove that p(x, y) = p(x|y, z)p(y|z). b) Use part a) to show that p(yla, 2): = p(x|y, z)p(y|2) p(x|z) (7) (8) a) Let X, Y, Z be random variables. Letr, y, z be the realized values of the random variables X, Y, Z. Use the definitions of conditional probabilities to prove that p(x, y) = p(x|y, z)p(y|z). b) Use part a) to show that p(yla, 2): = p(x|y, z)p(y|2) p(x|z) (7) (8)

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