7 A random variable \(X\) has probability density function defined by
$$f ( x ) = \begin{cases} k \left( \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x ^ { 3 } } \right) & 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{cases}$$
where \(k\) is a constant.
- Show that \(k = \frac { 8 } { 7 }\).
- Find \(\mathrm { E } ( X )\).
- Three values of \(X\) are chosen at random. Find the probability that one of these values is less than 1.5 and the other two are greater than 1.5.
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