3. A random variable \(X\) has probability density function given by $$f ( x ) = \begin{cases} k x ^ { 2 } & 0 \leqslant x \leqslant 2
k \left( 1 - \frac { x } { 6 } \right) & 2 < x \leqslant 6
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.

1. Show that \(k = \frac { 1 } { 4 }\)
2. Write down the mode of \(X\).
3. Specify fully the cumulative distribution function \(\mathrm { F } ( x )\).
4. Find the upper quartile of \(X\).