The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by f(x) = αe-(1/5)x, x > 0 0, elsewhere.
Find
(a) The value of α that makes f(x) a probability density function.
(b) The probability that this individual will talk (i) between 8 and 12 minutes, (ii) less than 8 minutes, (iii) more than 12 minutes.
(c) Find the cumulative distribution function, F(x).