5 The independent discrete random variables \(U\) and \(V\) can each take the values 1, 2 and 3, all with probability \(\frac { 1 } { 3 }\). The random variables \(X\) and \(Y\) are defined as follows: $$X = | U - V | , Y = U + V .$$

1. In the Printed Answer Book complete the table showing the joint probability distribution of \(X\) and \(Y\).
2. Find \(\operatorname { Cov } ( X , Y )\).
3. State with a reason whether \(X\) and \(Y\) are independent.
4. Find \(\mathrm { P } ( Y = 3 \mid X = 1 )\).