3 The continuous random variable \(T\) has probability density function given by $$\mathrm { f } ( t ) = \begin{cases} 0 & t < 0 ,
\frac { a } { \mathrm { e } } & 0 \leqslant t < 2 ,
a \mathrm { e } ^ { - \frac { 1 } { 2 } t } & t \geqslant 2 , \end{cases}$$ where \(a\) is a positive constant.

1. Show that \(a = \frac { 1 } { 4 } \mathrm { e }\).
2. Find the upper quartile of \(T\).