
| P(.) | |
| U = 0 | 0.5 |
| U = 1 | 0.5 |
| P(V = 0| .) | P(V = 1| .) | |
| U = 0 | 0.5 | 0.5 |
| U = 1 | 0.5 | 0.5 |
| P(W = 0| .) | P(W = 1| .) | |
| U = 0 | 1 | 0 |
| U = 1 | 0 | 1 |
| P(Z = 0| .) | P(Z = 1| .) | ||
| V = 0 | W = 0 | 0.5 | 0.5 |
| V = 0 | W = 1 | 1 | 0 |
| V = 1 | W = 0 | 1 | 0 |
| V = 1 | W = 1 | 0.5 | 0.5 |
If the probability function for a random variable \( x \) is given as \( f(x) = \frac{x+3}{15} \) when \( x = 1, 2, 3 \), find the sum of the values of the probability distribution for \( x \).