7 The lifetime, \(x\) years, of the power light on a freezer, which is left on continuously, can be modelled by the continuous random variable with density function given by
$$\mathrm { f } ( x ) = \begin{cases} k \mathrm { e } ^ { - 3 x } & x > 0
0 & \text { otherwise } \end{cases}$$
where \(k\) is a constant.
- Show that \(k = 3\).
- Find the lower quartile.
- Find the mean lifetime.