## PhoenixFire 3 years ago How do I find the lifetime of a component with reliability function: \[R(t)=e^{-0.01t}\] I calculated the probability density function: \[f(t)=-0.01e^{-0.01t}\]

1. Zarkon

why is your probability density function negative?

2. PhoenixFire

Ah yes... okay, so the pdf is \[f(t)=0.01e^{-0.01t}\] My bad I messed something up. So now how do I find the lifetime of that component? I'm a little confused with this probability stuff.

3. Zarkon

are you looking for the average lifetime?

4. PhoenixFire

The lifetime T (in days) of an electrical component has reliability function given by: R(t) = e^0:01t for time t > 0. An electrical system consists of four such components. The system continues to function if at least one component is still `alive' and the system is repaired (by replacing all the components) when all components have expired. (a) Find the probability density function (PDF) of T, the lifetime of a component in the system. f(t)=0.01e^(-0.01t)

5. PhoenixFire

Ah... i read the question wrong.. that equation is the lifetime equation.. then for (b) Show that this is a valid PDF. ... how do I do this?