Exam Style Question, CH4 - Reinsurance

The exam style question in Chapter 4 part (ii) asks us to calculate the likelihood of the data and gives information that 10 claims were received, 4 of which involved the reinsurer.

In the solution, it considers the 6 claims which are <M and do not involve the reinsurer. ie. they calculate Pr(X<M)^(n-m). However, in the core reading on page 24 of Chapter 4, to calculate the likelihood, they consider the claims that do involve the reinsurer, ie. they calculate Pr(X>M)^m.

Is my reasoning correct that one of these has to be wrong or am I confused somewhere along the line.

Thanks.

 

If a) I understand what you are asking and b) my memory of that material is sufficiently good (I got an exemption from Uni),

I would have thought that it would have involved a product of the 2 items you have there along with a 10 C 4 factor.
ie P(X<=m)^(n-x)*P(X>m)^x* (n C x), observed value of x is 6, n=10.

Of course if you (or the question) mean by "calculate the likelihood", calculate a function of the likelihood in order to maximise it (rather than the absolute number = likelihood), then you could always knock off constants like the n C x.
(I originally had 10 C 4 but thought that it should be n C x, which then made it non-constant. However I think in maximising likelihoods the x is known and then we can treat it all as constants, The variable being the parameters of the distribution)

Who knows (and I'm really guessing here), if you play with it long enough you could even find a constant to knock off that allows you to just include the P(X>m)^x

Hope that helps some. Does that make any sense at all? The more I think about it myself the worse it seems to me.

 

This does clear it up - Thanks John.