Problem 4. Consider the joint pmf given in the table below. 1 2 Pxy(x,y) 1 2 a 2a За b 26 3b 3 1. What conditions a and

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Problem 4. Consider the joint pmf given in the table below. 1 2 Pxy(x,y) 1 2 a 2a За b 26 3b 3 1. What conditions a and b must satisfy for this to be a valid pmf? 2. Give two sets of examples of a and b for which the pmf is valid. 3. For any such choice making the above pmf valid, are X and Y independent? Provide formal justification by checking if Pxy(x, y) = Px(x)py(y) for at least two pairs of choices of x and y.