The useful life X of a particular kind of machine is a random variable with density function f(x)={(3/(x^2))+(1/6) if 3≤x≤6 and 0 if otherwise} where x is the number of years a randomly selected machine stays in use.
(a) Find the probability that a randomly selected machine will be useful for more than 4 years. _________
(b) Find the probability that a randomly selected machine will be useful for less than 5 years. __________
(c) What is the expected useful life of the machine? 4.3294 (CORRECT)