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# Question

Suppose that each of two urns has four chips, numbered 1 through $$4 .$$ A chip is drawn from the first urn and bears the number $$X$$. That chip is added to the second urn. A chip is then drawn fromthe second urn. Call its number $$Y$$.(a) Find $$p_{X, Y}(x, y)$$.(b) Show that $$p_{X}(k)=p_{Y}(k)=\frac{1}{4}, k=1,2,3,4$$.(c) Show that $$X$$ and $$Y$$ are not independent.

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