5 The discrete random variable \(X\) has the following probability distribution.
| \(\boldsymbol { x }\) | \(\mathbf { 2 }\) | \(\mathbf { 4 }\) | \(\mathbf { 6 }\) | \(\mathbf { 9 }\) |
| \(\mathbf { P } ( \boldsymbol { X } = \boldsymbol { x } )\) | 0.2 | 0.6 | 0.1 | 0.1 |
5
- Find \(\mathrm { P } ( X \leq 6 )\)
5
- Let \(Y = 3 X + 2\)
Show that \(\operatorname { Var } ( Y ) = 32.49\)
5 - The continuous random variable \(T\) is independent of \(Y\).
Given that \(\operatorname { Var } ( T ) = 5\), find \(\operatorname { Var } ( T + Y )\)