I have function as following $d(a,b):=pr(x-a>max{(y-b,0)})$ where a and b are constant and x and y are random variable. As this is a max function, it will have kink point hence, will not be deferentiable at all points with respect to a and b.
But from probability class I took, given that a and b are independent, that function can be rewritten as $d(a,b)=pr(x-a>y-b)\cdot pr(x-a>0)$ which looks differentiable.
Can i differentiate any of both functions at any point? Neither can be differentiated?
Is there any way to make that to be differentiated?
Thanks