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
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)
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
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.
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.
