Suppose that the duration in minutes of long-distance telephone calls made from a certain city is found to be a random phenomenon, with a probability function specified by the distribution function F(), given by
![716_minutes of long-distance telephone calls.png](https://secure.tutorsglobe.com/CMSImages/716_minutes of long-distance telephone calls.png)
(i) Sketch the distribution function.
(ii) Is the distribution function continuous? Discrete? Neither?
(iii) What is the probability that the duration in minutes of a long-distance telephone call will be (a) more than 6 minutes, (b) less than 4 minutes, (c) equal to 3 minutes, (d) between A and 7 minutes?
(iv) What is the conditional probability that the duration of a long distance telephone call will be (a) less than 9 minutes, given that it has lasted more than 5 minutes, (b) less than 9 minutes, given that it has lasted more than 15 minutes?