1. A continuous random variable \(X\) has cumulative distribution function \(\mathrm { F } ( x )\) given by

$$\mathrm { F } ( x ) = \left\{ \begin{array} { c r } 0 & x < - 1
\frac { 1 } { 5 } ( x + 1 ) ^ { 2 } & - 1 \leqslant x \leqslant 0
1 - \frac { 1 } { 20 } ( 4 - x ) ^ { 2 } & 0 < x \leqslant 4
1 & x > 4 \end{array} \right.$$

1. Find the probability density function, \(\mathrm { f } ( x )\)
2. 1. Sketch \(\mathrm { f } ( x )\)
   2. Hence describe the skewness of the distribution.
3. Find, to 3 significant figures, the value of \(c\) such that $$\mathrm { P } ( 1 < X < c ) = \mathrm { P } ( c < X < 2 )$$