8 The lifetime, in years, of an electrical component is the random variable \(T\), with probability density function f given by
$$\mathrm { f } ( t ) = \begin{cases} A \mathrm { e } ^ { - \lambda t } & t \geqslant 0
0 & \text { otherwise } \end{cases}$$
where \(A\) and \(\lambda\) are positive constants.
- Show that \(A = \lambda\).
It is known that out of 100 randomly chosen components, 16 failed within the first year.
- Find an estimate for the value of \(\lambda\), and hence find an estimate for the median value of \(T\).