4. The continuous random variable, \(X\), has the following probability density function $$f ( x ) = \begin{cases} k x & \text { for } 0 \leqslant x < 1
k x ^ { 3 } & \text { for } 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$ where \(k\) is a constant.
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1. Show that \(k = \frac { 4 } { 17 }\).
2. Determine \(\mathrm { E } ( X )\).
3. Calculate \(\mathrm { E } ( 3 X - 1 )\) and \(\operatorname { Var } ( 3 X - 1 )\).