5 The continuous random variable \(X\) has probability density function
$$f ( x ) = \begin{cases} x ^ { 3 } & 0 < x \leq 1
\frac { 9 } { 1696 } x ^ { 3 } \left( x ^ { 2 } + 1 \right) & 1 < x \leq 3
0 & \text { otherwise } \end{cases}$$
5
- Find \(\mathrm { P } ( X < 1.8 )\), giving your answer to three decimal places.
[0pt]
[3 marks]
5 - Find the lower quartile of \(X\)
| 5 | 5- Show that \(\mathrm { E } \left( \frac { 1 } { X ^ { 2 } } \right) = \frac { 133 } { 212 }\)
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