5. The discrete random variable \(X\) has the following probability distribution
| \(x\) | - 2 | 0 | 2 | 4 |
| \(\mathrm { P } ( X = x )\) | \(a\) | \(b\) | \(a\) | \(c\) |
where \(a\), \(b\) and \(c\) are probabilities.
Given that \(\mathrm { E } ( X ) = 0.8\)
- find the value of \(c\).
Given also that \(\mathrm { E } \left( X ^ { 2 } \right) = 5\) find
- the value of \(a\) and the value of \(b\),
- \(\operatorname { Var } ( X )\)
The random variable \(Y = 5 - 3 X\)
Find - \(\mathrm { E } ( Y )\)
- \(\operatorname { Var } ( Y )\)
- \(\mathrm { P } ( Y \geqslant 0 )\)