Avi
07-14-2003, 05:47 PM
Claim Sizes have the following Distribution:
Amount Paid # of Payments
0 - 500 60
500 - 1000 35
1000 - 2000 5
Let X be claim size.
Calculate E[ (X Λ 1000)²] using the empirical distribution.
The answer given is 304,166.6666 and is obtained as:
[1/(100*3) * { (60*500³/500) + (35*(1000³-500³)/500)}] + 5*1000²/100
Now I realize we can't just use average payment, as we are trying to get an expected value of a sum of squares, not just of the payments. But can someone please explain where the first part of this answer is coming from (the second term is just taking the 1000 limit into account)?
Thank you
Amount Paid # of Payments
0 - 500 60
500 - 1000 35
1000 - 2000 5
Let X be claim size.
Calculate E[ (X Λ 1000)²] using the empirical distribution.
The answer given is 304,166.6666 and is obtained as:
[1/(100*3) * { (60*500³/500) + (35*(1000³-500³)/500)}] + 5*1000²/100
Now I realize we can't just use average payment, as we are trying to get an expected value of a sum of squares, not just of the payments. But can someone please explain where the first part of this answer is coming from (the second term is just taking the 1000 limit into account)?
Thank you