2. The discrete random variable \(Q\) has the following probability distribution.
| \(q\) | 1 | 2 | 3 | 4 | 5 |
| \(\mathrm { P } ( Q = q )\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) |
- Write down the name of this distribution.
The discrete random variable \(R\) has the following probability distribution.
| \(r\) | 14 | 24 | 34 | 44 | 54 |
| \(\mathrm { P } ( R = r )\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) | \(\frac { 1 } { 5 }\) |
- State the relationship between \(R\) and \(Q\) in the form \(R = a Q + b\).
Given that \(\mathrm { E } ( Q ) = 3\) and \(\operatorname { Var } ( Q ) = 2\),
- find \(\mathrm { E } ( R )\) and \(\operatorname { Var } ( R )\).