Adevice containing two key components fails when and only when both components fail. the lifetimes, t1 and t2, of these components are independent with common density function f(t)=e^-t for t > 0. the cost, x, of operating the device until failure is 2t1 + t2.
1. what is the density function of x for x > 0?

Step-by-step explanation:

If we have two random variables Y1 and Y2 and we have th following limits:

We an find the density function with this formula:

Now for our problem we know that for the two times of failure the density function is given by:

And we know that the joint density for T1 and T2 is given by:

And we know that

If we solve for

And then we can find the density function like this:

if x = 1, then the answer is 3.5