Bounds Question

[giantnelson]

I was working on the 124 sample questions. Problem 108 and 109 are basically the same problem, just a few algebraic differences. However, in the solutions pdf for 108 the outside integral has bounds of 0 to x, where in 109 the bounds are 0 to infinity. I can't see any difference in these two problems that would make the bounds different. I was wondering if someone could shed some light as to what the difference is. What am I not seeing here? Thanks.

[daaaave]

As a side note, if you go to the Spring 2008 catalog on the SOA webpage, there are now 127 sample questions. I don't have a link handy, but will add one when I get home.

The difference here comes from the combination that we are considering and becomes apparent if you draw a picture. In #108, X is the sum of two random variables, and the region X<=x corresponds to a bounded triangle in terms of the orignal variables. In #109, X is the ratio of two random variables, and if you draw a plane with premiums on one axis and claims on the other, the set X<=x will no longer correspond to a bounded region.

I'll try to remember to add a picture that will clarify this tonight.

[daaaave]

I've attached a picture that should be consistent with the sample solutions. The Spring 2008 syllabus, which has links to the expanded (127) sample problems is at http://www.soa.org/files/pdf/edu-2008-spring-exam-p.pdf

[giantnelson]

Thanks Dave!