- The discrete random variable \(X\) has probability distribution
| \(x\) | - 2 | - 1 | 1 | 2 | 3 |
| \(\mathrm { P } ( X = x )\) | \(b\) | \(a\) | \(a\) | \(b\) | \(\frac { 1 } { 5 }\) |
where \(a\) and \(b\) are constants.
- Write down an equation for \(a\) and \(b\).
- Calculate \(\mathrm { E } ( X )\).
Given that \(\mathrm { E } \left( X ^ { 2 } \right) = 3.5\)
- find a second equation in \(a\) and \(b\),
- hence find the value of \(a\) and the value of \(b\).
- Find \(\operatorname { Var } ( X )\).
The random variable \(Y = 5 - 3 X\)
- Find \(\mathrm { P } ( Y > 0 )\).
- Find
- \(\mathrm { E } ( Y )\),
- \(\operatorname { Var } ( Y )\).