The amount of time (in minutes) that an executive of a certain firm talks on the telephone is a random variable having the probability density
![](https://test.transtutors.com/qimg/308024ec-f9fb-47cf-9080-ab54094270dd.png)
With reference to part (b) of Exercise 60, find the expected length of one of these telephone conversations that has lasted at least 1 minute.
Exercise 60
(a) Show that the conditional distribution function of the continuous random variable X, given a ? b, is given by
![](https://test.transtutors.com/qimg/c50527e1-a219-4447-a829-d7423ba5066a.png)
(b) Differentiate the result of part (a) with respect to x to find the conditional probability density of X given a ? b, and show that
![](https://test.transtutors.com/qimg/4cddf539-8c1a-4616-b81a-9b7168eb63e2.png)