2 The independent discrete random variables \(X\) and \(Y\) can take the values 0,1 and 2 with probabilities as given in the tables.
| \(x\) | 0 | 1 | 2 |
| \(\mathrm { P } ( X = x )\) | 0.5 | 0.3 | 0.2 |
\(\quad\)
| \(y\) | 0 | 1 | 2 |
| \(\mathrm { P } ( Y = y )\) | 0.5 | 0.3 | 0.2 |
The random variables \(U\) and \(V\) are defined as follows:
$$U = X Y , V = | X - Y | .$$
- In the Printed Answer Book complete the table giving the joint distribution of \(U\) and \(V\).
- Find \(\operatorname { Cov } ( U , V )\).
- Find \(\mathrm { P } ( U V = 0 \mid V = 2 )\).