Question: 2.9 The random variables X and Y have the joint distribution X 123 12 1 12 1 6 1 12 Y 13 1 3 0

2.9 The random variables X and Y have the joint distribution X

123 12 1 12 1

6 1

12 Y 13 1 3 0 0 44 1 9

1 9

1 9

a) Calculate the marginal distributions of X and Y.

b) Show that the random variables X and Y are dependent.

c) Find two random variables U and V which have the same marginal distributions as X and Y but are independent.

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