Nov 13 -IAI paper

Can anyone help me on q 7 of the iai nov 13 CT 3 paper.
The link of the paper is
http://actuariesindia.org/subMenu.aspx?id=278&val=Paper_for_Nov_2013

I felt many questions were not what I studied from the core reading.

 

I did not write this paper. I cleared CT7 in the May diet. The answer to Q7 should be A - Only variable costs should be considered as per the Bygones principle.

 

He's asking CT3 doubts

You didn't practiced UK past papers?? Have a look at Q2 of this April 13 paper.

Here -http://www.actuaries.org.uk/research-and-resources/documents/subject-ct3-probability-and-mathematical-statistics-exam-paper-apri

Soln here - http://www.actuaries.org.uk/research-and-resources/documents/subject-ct3-probability-and-mathematical-statistics-examiners-repor

Very similar to the one you've asked. Let me know if you still find any difficulty in solving the question you've put up after looking at this past question..

For part (ii) - After we've proved that X ~ N(0,1).. just use Inverse Transformation method to simulate values from X i.e.
Equate
P(X< x1) = 0.619
P(X< x2) = 0.483

and find x1 and x2 by using standard normal tables. Interpolation maybe required.

You can't expect all questions to be straightforward
There will always be 2-3 tricky questions. You just have to be prepared for them..

 

OMG. I was totally lost. Wonder how many such mistakes I made on the exam too

 

You are absolutely right suraj.
Will need a lot of practice on these tricky questions.
Thanks for the help.

 

I think you need not solve this way. Notice the word 'Hence' at the start of part (ii) in the question.

I think what the examiners wanted is to merely substitute the values of U in the form of X given in the question and find the value of X from the tables. Looking at the values of U, I think one can find the values of X directly.

Further for solving part (ii), you need not solve part (i).

 

That 'hence' came after part (i) in which we've showed that X is standard normal. Now using this fact we've to simulate values from X.

Otherwise part (ii) would've been in place of (i) and vice-versa.

I do agree with you that one can completely ignore part(i) and plug those u's given in part(ii) in the original form of X to simulate values. This will give different values as compared to Inverse Transformation - but that doesn't matter..

 

Not sure I completely agree with your interpretation of 'Hence'.
Then again it does not matter to me.

 

I think suraj's argument is sound. However, I suspect that when the examiners wrote "Hence" they meant you to use the information in the question, not the information from part i) and hadn't quite appreciated the fact that this isn't the most logical interpretation.

It's remarkably easy to get this kind of thing wrong when setting questions. For example, the draft paper may have had the parts the other way round. It gets reviewed and somebody suggests swapping them. It doesn't then get reviewed again so nobody picks up on the fact that the question now doesn't read as intended.

 

My take is simple .. The question asks to simulate two values from the random variable X (which has a relationship with U in the given form).

Otherwise it would have just ask you to simulate two observations from a standard normal random variable !

 

IMO both methods are correct & as I've said earlier that it doesn't matter if you're getting different set of values using both methods. Both should be deemed correct. It's just that, using X as N(0,1) came to my mind first after looking at part (i) so I suggested that in my first post..

 

Whatever is the reason i found questions regarding simulations (especialy when the uniform distributions are involved) always puzzling. So had to leave part ii
For part 1 apart for the similarity between UK question.

Can anyone also tell the approch to Q6 (Part ii and iii). I think there was an element of conditional involved here.


(4,5,6,7) goofed up. Hoping for the remainder to be true

 

Consider one policy at a time. Say take j_th policy.
Denote S_j as the amount claimed for that policy.

You have expressions for E(S_j) and Var(S_j) from part (i).

T is the total claim for 100 policies. Thus, T = sum of S_j for j: 1 to 100. E(T) and Var(T) follows using the fact all policies are independent.

 

oh seems I have done it for 1 policy