Suppose the lifetime of a radio is a random variable T, with the following p.d.f.
- f(x) = 0 if x < 5 = 50/x^3 if x ≥ 5.
(a) What is the average life time of the radio?
(b) Find the cumulative distribution function F for the lifetime of the radio.
(c) If you buy a new radio, what is the probability that it works for more than 15 years (that is P (T > 15))?
(d) If you buy a 10-years-old radio, what is the probability that it works for 15 more years (that is, more than 25 years in total)? Do you prefer a new radio or a 10-years-old radio? Use the formula you found in the last problem.