1. The continuous random variable \(X\) has cumulative distribution function given by

$$\mathrm { F } ( x ) = \left\{ \begin{array} { c r } 0 & x < 3
\frac { 1 } { 6 } ( x - 3 ) ^ { 2 } & 3 \leqslant x < 4
\frac { x } { 3 } - \frac { 7 } { 6 } & 4 \leqslant x < c
1 - \frac { 1 } { 6 } ( d - x ) ^ { 2 } & c \leqslant x < 7
1 & x \geqslant 7 \end{array} \right.$$ where \(c\) and \(d\) are constants.

1. Show that \(c = 6\)
2. Find \(\mathrm { P } ( X > 3.5 )\)
3. Find \(\mathrm { P } ( X > 4.5 \mid 3.5 < X < 5.5 )\)