- The lifetime of a single component has cumulative distribution function .

The lifetime of the system has cumulative distribution function .

Notice since that for all .

- The mean lifetime of a single component is .

The mean lifetime of the system is .

But for all .

Thus .- The median lifetime of a single component is where .

The median lifetime of the system is where .

But , so that .

- It is well known that .

Now .

Also ,

and so .

Therefore .