Hi to all. I have the following past exam question:
"For a portfolio of risks, all members' aggregate losses per year per exposure have a normal distribution with a standard deviation of 1000. For these risks, 60% have a mean of 2000, 30% have a mean of 3000, and 10% have a mean of 4000. A randomly selected risk had the following experience over three years. In year 1, there were 24 exposures with total losses of 24000. In year 2, there were 30 exposures with total losses of 36000. In year 3, there were 26 exposures with total losses of 28000. Determine the Buhlmann-Straub estimate of the mean aggregate loss per year per exposure for year 4."
The problem I have is the following:
Does the first sentence state the following:
let S=(X1+X2+...+Xm)/m be our aggregate loss per year per exposure unit
then S~Normal(M, 1000^2)?
If so, then this implies that Var(S)=Var(X)/m=1000^2 and to solve for the Buhlmann-Straub model we need Var(X) not Var(S). How do I obtain Var(X) without knowing m?
Thanks to any hints/answers
"For a portfolio of risks, all members' aggregate losses per year per exposure have a normal distribution with a standard deviation of 1000. For these risks, 60% have a mean of 2000, 30% have a mean of 3000, and 10% have a mean of 4000. A randomly selected risk had the following experience over three years. In year 1, there were 24 exposures with total losses of 24000. In year 2, there were 30 exposures with total losses of 36000. In year 3, there were 26 exposures with total losses of 28000. Determine the Buhlmann-Straub estimate of the mean aggregate loss per year per exposure for year 4."
The problem I have is the following:
Does the first sentence state the following:
let S=(X1+X2+...+Xm)/m be our aggregate loss per year per exposure unit
then S~Normal(M, 1000^2)?
If so, then this implies that Var(S)=Var(X)/m=1000^2 and to solve for the Buhlmann-Straub model we need Var(X) not Var(S). How do I obtain Var(X) without knowing m?
Thanks to any hints/answers
Buhlmann-Straub Exam Question
