Question: 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

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

p (х,у) х y -1 1 1/3 1/3 1/3

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.

p (,) y -1 1 1/3 1/3 1/3

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