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
(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?