I am really struggling with comprehending joint distributions. Here is a question that I want to understand. I am not too fussed whether anybody gives me the actual answer!
Suppose 2 components have independent exponentially distributed lifetimes and with parameters .
I understand that the independence of allows me to find the joint distribution. So I can say:
I am having a difficult time understanding why to find I then stick the above in between double integrals and evaluate.
I am also struggling with the limits on the integrals (not just with their LaTex representation!)
Can someone english-ify this for me?