4 A continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} \frac { 3 } { 16 } ( x - 2 ) ^ { 2 } & 0 \leqslant x \leqslant 4
0 & \text { otherwise } \end{cases}$$
- Sketch the graph of \(y = \mathrm { f } ( x )\).
- Calculate the variance of \(X\).
- A student writes " \(X\) is more likely to occur when \(x\) takes values further away from 2 ". Explain whether you agree with this statement.