4. The discrete random variable \(X\) has probability distribution
| \(x\) | - 4 | - 3 | 1 | 2 | 5 |
| \(\mathrm { P } ( X = x )\) | \(a\) | \(b\) | \(a\) | \(b\) | 0.2 |
- Find \(\mathrm { E } ( X )\) in terms of \(a\) and \(b\)
For this probability distribution, \(\operatorname { Var } ( X ) = \mathrm { E } \left( X ^ { 2 } \right)\)
- Write down the value of \(\mathrm { E } ( X )\)
- Find the value of \(a\) and the value of \(b\)
- Find \(\operatorname { Var } ( 1 - 3 X )\)
Given that \(Y = 1 - X\), find
- \(\mathrm { P } ( Y < 0 )\)
- the largest possible value of \(k\) such that \(\mathrm { P } ( Y < k ) = 0.2\)