You are a manufacturer of electronic devices. The lifetimes of your devices foll

Question

You are a manufacturer of electronic devices. The lifetimes of your devices
follow a certain probability density p(t), whose cumulative distribution function is given
by
P(t) = a(1 ? e^(?5t))

for t ? 0,
where a is a constant and t is the time in years. For t < 0, P(t) = 0.
(a) Find a so that P(t) is indeed a cumulative distribution function.
(b) Find the median lifetime of your devices.
(c) What fraction of devices stop working within one year after the date of manufacturing?

Explanation / Answer

(a) P(t) has to tend to 1 for t -> infinity , so a = 1. (b) P(T) = 1/2 if T = ln 2 / 5. (c) This quantity is given by P(1) = 1 - e^-5.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.