Question: The joint probability distribution of two random variables X and Y is given in the following table. Y -1 2 X -1 0.1 0.1 -2

The joint probability distribution of two random variables X and Y is given in the following table.

		Y
		-1	2
X	-1	0.1	0.1
	-2	0.5	0.1

1. Calculate the marginal probability distribution of X. 2. Calculate the marginal probability distribution of Y. 3. Calculate E( X ) and s.d.( X ). 4. Calculate E( Y ) and s.d.( Y ) 5. Calculate cov(X, Y) and corr(X, Y). 6. Calculate the conditional probability distribution of X given Y = -1. 7. Calculate the conditional probability distribution of X given Y = 2. 8. Calculate E( X | Y = -1 ) and var( X | Y = -1 ). 9. Calculate E( X | Y = 2 ) and var( X | Y = 2 ). 10. Verify the Law of Iterated Expectations E(X)=E[E(X|Y)] by using your previous results. 11. Are X and Y independent random variables? Justify your answer based on answers to the preceding questions.

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