Here are two random variables that are uncorrelated but not independent. Let X and Y have the following joint probability mass function:





a. Use the definition of independence on page 141 to show that X and Y are not independent (in fact Y=|X|, so Y is actually a function of X).

b. Show that X and Y are uncorrelated.


(a) P(X = 1) = 1/3, ?(Y = 1) = 2/3, P(X = 1 and Y = 1) = 1/3 ?P(X = 1)?(Y = 1).



(b)

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