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Independence. Suppose X and Y are independent. Let W = h(X) and Z = l`(Y )...

Independence. Suppose X and Y are independent. Let W = h(X) and Z = l`(Y ) for some functions h and `. Make use of IEf(X)g(Y ) = IEf(X)IEg(Y ) for all f and g greater or equal to 0 types of random variables, not just discrete random variables. a) Show that X and Z are independent. b) Show that W and Z are independent. c) Suppose Z = l`(Y ) and all we know is that X and Z are independent. Does that imply that X and Y are independent? Justify your answer with a proof or a counterexample.

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