1 The random variable \(W\) can take values 1,2 or 3 and has a discrete uniform distribution.
- Write down the value of \(\mathrm { E } ( 2 W )\).
- Find the value of \(\operatorname { Var } ( 2 W )\).
- Determine the value of the constant \(k\) for which \(\mathrm { E } ( 2 \mathrm {~W} + \mathrm { k } ) = \operatorname { Var } ( 2 \mathrm {~W} + \mathrm { k } )\).
The random variable \(S\) has the probability distribution shown in the following table.
| \(S\) | 2 | 3 | 4 | 5 | 6 |
| \(P ( S = S )\) | \(\frac { 2 } { 9 }\) | \(\frac { 1 } { 9 }\) | \(\frac { 1 } { 3 }\) | \(\frac { 1 } { 9 }\) | \(\frac { 2 } { 9 }\) |
- Calculate \(\operatorname { Var } ( S )\).