The probability of a claim is q. The sitribution function for the size of a claim is F(x). The probability that the amount paid exceeds L, given that a claim occurs is: 1- F(x). Why not (1-F(x)) / q? This was a multiple choice question and my answer was (1-F(x)) / q but the actual answer is 1-F(x).
F(x) is the distribution of the claim given that a claim has occurred. Since you are told that a claim has occurred, q doesn't enter into it.
Sorry, I messed up the answers: As pointed out below the correct answer is: 1-F(L) I chose (1- F(L))/q which is wrong This was question 1 on April 1998.
The F(x) is the distribution of a claim. If there is no claim then you don't need a distribution for it. Hence the F(x) is the distribution of a claim given that it occurs. You're confusing it with the case where as claim has occured but it is over the retention limit (or excess). In which case the F(x) on its own doesn't give that and so we need the conditional thing.
