3 The probability density function of the continuous random variable \(X\) is given by $$\mathrm { f } ( x ) = \begin{cases} c + x & - c \leqslant x \leqslant 0
c - x & 0 \leqslant x \leqslant c
0 & \text { otherwise } \end{cases}$$ where \(c\) is a positive constant.

1. (A) Sketch the graph of the probability density function.
   (B) Show that \(c = 1\).
2. Find \(\mathrm { P } \left( X < \frac { 1 } { 4 } \right)\).
3. Find
   • the mean of \(X\),
   • the standard deviation of \(X\).