I'm wondering if someone can check me work to see if I in fact have the correct solution.
U=Y_1-Y_2
A remark: the density is positive on a neighbourhood of , so that and can both be close to zero. So that the probability density function of must be positive near zero. This does not hold with your solution. In addition, it seems you forgot the condition , didn't you?
You integral is in fact: if , , I think.
I was going more along the lines of the example in the book, which solves a problem like that in a similar fashion to what I have done.
I was thinking that I can just remove the bottom red triangle which goes from u to 2 on the line and 0 to leaving me only in the area in blue, which would be easier for me to solve, since I've never seen an integral that has a bound of min.