3 The continuous random variable \(X\) has a rectangular distribution defined by
$$\mathrm { f } ( x ) = \begin{cases} k & - 3 k \leqslant x \leqslant k
0 & \text { otherwise } \end{cases}$$
- Sketch the graph of f.
- Hence show that \(k = \frac { 1 } { 2 }\).
- Find the exact numerical values for the mean and the standard deviation of \(X\).
- Find \(\mathrm { P } \left( X \geqslant - \frac { 1 } { 4 } \right)\).
- Write down the value of \(\mathrm { P } \left( X \neq - \frac { 1 } { 4 } \right)\).
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