Deductible + Policy Limit Question

Hi guys,



This may be a very trivial question, but I can't seem to figure it out. Why does a deductible, d combined with a policy limit u, give an expected payment per loss of



E(X^u) - E(X^d)?



(I can't find the symbol for limit "^" - the legs supposed to go to the ground - you get what I mean...)



What I got so far....



So the payment per loss would be



0 for X<d

X-d for d<X<u+d

u for X>u+d



So I want E(X-d | d<X<u+d)P(d<X<u+d) + u*P(X>u+d)



I give up :oops:

Deductible + Policy Limit Question