- The waiting times, in minutes, between flight take-offs at an airport are modelled by the continuous random variable \(X\) with probability density function
$$f ( x ) = \begin{cases} \frac { 1 } { 5 } & 2 \leqslant x \leqslant 7
0 & \text { otherwise } \end{cases}$$
- Write down the name of this distribution.
A randomly selected flight takes off at 9am
- Find the probability that the next flight takes off before 9.05 am
- Find the probability that at least 1 of the next 5 flights has a waiting time of more than 6 minutes.
- Find the cumulative distribution function of \(X\), for all \(x\)
- Sketch the cumulative distribution function of \(X\) for \(2 \leqslant x \leqslant 7\)
On foggy days, an extra 2 minutes is added to each waiting time.
- Find the mean and variance of the waiting times between flight take-offs on foggy days.