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Chapter 6 risk models (1) Q6.8

M

mugono

Ton up Member
Good evening all,

I was hoping whether somebody could help me with this question. For convenience, I write the question here:

A compound distribution S is such that P(N=0) = 0.6, P(N=1) = 0.3 and P(N=2) = 0.1. Claim numbers are either 1 unit or 2 units, each with probability 0.5. Derive the distribution function of S

I have two main problems with this question.

The solution given for this question states that the aggregate claim amount S can take the values 0,1,2,3 or 4

(a) How are you able to tell from the question that the aggregate claim amount takes ONLY 0,1,2,3 or 4? Why is it unable to take any bigger value?

(b) For P(S less than or equal to 3) = P(S less than or equal to 3) + 0.1 x 2 x 0.5^2

I am having trouble obtaining the second part of this equation. Could somebody please explain how this is obtained?

Any help would be much appreciated. :)
 
Tutor's??

Could a tutor help with the question I posted in the previous thread??

Any help would be much appreciated
 
Hi Mugono,

Surprised no-one has answered this one yet - must be a particularly tough one!

From what I remember of CT6, I can help with your first question. There can only be 0, 1 or 2 claims (N=0, N=1 or N=2) and the claim amounts can only be 1 or 2. So the aggregate claim amount can only take the values 0, 1, 2, 3 or 4 (ie, if there are 2 claims of 2, aggregate value would be 4 - that is the maximum possible in this scenario).

Hope that helps with the first part and maybe helps you to understand what is going on in this question. I don't really follow your second question so can't help with that - can anyone else help?
 
Hello Mugono

Ricegirl has given a great response to your first query.:D

As for your second query, I think we are being thrown by what you wrote down???

Did you mean to write:

P(S less than or equal to 3) = P(S less than or equal to 2) + 0.1 x 2 x 0.5^2?

This comes from P(S less than or equal to 3) = P(S less than or equal to 2) + P(S equal to 3)

So we need to work out why P(S equal to 3) = 0.1 x 2 x 0.5^2

Well, how do you get to a total of 3? We would have to have two claims in total (N = 2), one claim for an amount 1 (X = 1) and one claim for an amount 2 (X = 2).

Working out the probability of N = 2, X = 1 and X = 2 we get:

0.1 x 0.5 x 0.5

But the two claims can happen in either order (X = 1 then X = 2 or X = 2 then X = 1). This is where the extra 2 comes from.

Is this ok now?:rolleyes:

Anna
 
Thank you Anna and Ricegirl. Both answers do make sense! Apologies for the typo in my original question, Anna you were right I meant to write 2 and not 3

I really do appreciate the time taken to help me

;)
 
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