CT6 Reinsurance

[Bharti Singla]

Hi all
Please clarify following two things:
Ch. 4, Reinsurance pg 11- In qus. 4.6 , while estimating the parameters a denominator of n is used in the formula of variance. Why n is used instead of n-1?
pg16- The example given(below q.4.9) on this page asks for finding mean and variance, but in the solution only mean is calculated. Where is the variance?
Thanks

 

[Varsha Agarwal]

Q 4.6
When we calculated Variance for the sample data,where true mean population is estimated by sample mean we use (n-1)..This also means we have to infer more about population later.
On the other hand when we have enough sample data which can give the accurate variability,we use n to find Variance..also in this case we don't have to draw conclusion about population as its variance of population itself.
Q 4.9
In this case under treaty 1 Var(reinsurer)=.25*.25*.Var(of total claim)
its written sd(reinsurer)=.25*6408
Treaty 2: its simple found V(y)=E(y^2)-(E(y))^2,where E(y)was known and E(^2) is found integrating (x-m)^2 with pdf n limits.(Y is reinsurer)

 

[Bharti Singla]

Hi Varsha
In my second query, I am talking about the example (not the qus.) given on page 16, which is given below the qus. 4.9. The variance is not calculated in this example.
Thanks

 

[Bharti Singla]

And in Q.4.6, Can we also use n-1 as a denominator? Is there anything wrong using n-1? Also for which minimum value of n, we can say that the sample is enough to use n as a denominator in variance?

 

[Varsha Agarwal]

And in Q.4.6, Can we also use n-1 as a denominator? Is there anything wrong using n-1? Also for which minimum value of n, we can say that the sample is enough to use n as a denominator in variance?

If you use n-1 in denominator,Variance will be larger than before..It may not be fully wrong as answer will be close to it..Also there no minimum no of n fixed..it depends whether u have to draw conclusion for population from given sample or not..in this question not like that was mentioned so they used n as denominator.

 

[Varsha Agarwal]

Hi Varsha
In my second query, I am talking about the example (not the qus.) given on page 16, which is given below the qus. 4.9. The variance is not calculated in this example.
Thanks

Yes i saw its not calculated but you can do it yourself by finding E(X2^2) then variance of X2.

 

[Bharti Singla]

okay..thanks

 

[Varsha Agarwal]

okay..thanks

 

[John Lee]

n is used so that the two approaches (equating E(X), var(X) to sample mean & var or equating E(X), E(X²) to first two sample moments) are consistent.

In practice you could use either, however the examiners are testing the Core Reading - so they will require the use of n.

 

[Bharti Singla]

n is used so that the two approaches (equating E(X), var(X) to sample mean & var or equating E(X), E(X²) to first two sample moments) are consistent.

In practice you could use either, however the examiners are testing the Core Reading - so they will require the use of n.

Okay sir. Thanks