6 The continuous random variable \(T\) has probability density function defined by $$\mathrm { f } ( t ) = \left\{ \begin{array} { c c } \frac { 1 } { 3 } & 0 \leq t \leq \frac { 3 } { 2 }
\frac { 9 - 2 t } { 18 } & \frac { 3 } { 2 } \leq t \leq \frac { 9 } { 2 }
0 & \text { otherwise } \end{array} \right.$$ 6

1. 1. Sketch this probability density function below.
      \includegraphics[max width=\textwidth, alt={}, center]{6ccf7d1d-5a7b-47d1-b38e-c7e762204746-07_1009_1041_1073_520} 6
2. (ii) State the median of \(T\). 6
3. 1. Find \(\mathrm { E } ( T )\)
      [0pt] [2 marks]
      6
4. (ii) Given that \(\mathrm { E } \left( T ^ { 2 } \right) = \frac { 15 } { 4 }\), find \(\operatorname { Var } ( 4 T - 5 )\) [3 marks]