So, let's say that I was given two independent random variables ξ and η and...
So, let's say that I was given two independent random variables and and was told that has continuous distribution (basically, )
How can I prove that in such case their sum also will have continuous distribution? Problem that I have here is that I know that if two variables are independent then we can say , where stands for measures convolution operation, but I am nor really sure how to compute such a convolution. Can you provide some explanation or intuition on how to calculate such integrals? In my case I need to know integral like this:
And I have no rigorous way of showing that it is actually zero.