- The lifetime, in tens of hours, of a certain delicate electrical component can be modelled by the random variable \(X\) with probability density function
$$f ( x ) = \begin{cases} \frac { 1 } { 42 } x , & 0 \leq x < 6
\frac { 1 } { 7 } & 6 \leq x \leq 10
0 , & \text { otherwise } \end{cases}$$
- Sketch \(\mathrm { f } ( x )\) for all values of \(x\).
- Find the probability that a component lasts at least 50 hours.
A particular device requires two of these components and it will not operate if one or more of the components fail. The device has just been fitted with two new components and the lifetimes of these two components are independent.
- Find the probability that the device breaks down within the next 50 hours.