3. The lifetime, \(X\), in tens of hours, of a battery is modelled by the probability density function
$$f ( x ) = \left\{ \begin{array} { c c }
\frac { 1 } { 9 } x ( 4 - x ) & 1 \leqslant x \leqslant 4
0 & \text { otherwise }
\end{array} \right.$$
Use algebraic integration to find
- \(\mathrm { E } ( X )\)
- \(\mathrm { P } ( X > 2.5 )\)
A radio runs using 2 of these batteries, both of which must be working. Two fully-charged batteries are put into the radio.
- Find the probability that the radio will be working after 25 hours of use.
Given that the radio is working after 16 hours of use,
- find the probability that the radio will be working after being used for another 9 hours.