Problems in Markov chains - ku
for every (measurable) set A and ((Y,Z)(P)-almost) every (y,z). Thus if X and Y are conditionally independent given Z, then X is inde-pendent of Y given Z. Problem 1.4 Suppose that X, Y and Z are independent random variables. Show that (a) X and Y are conditionally independent given Z (b) X and X +Y +Z are conditionally independent given X +Y
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