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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

Abraham Weishaus
07-14-2003, 09:44 PM
Try the Klugman Course 3 study note formula 3.8 (which is just the definition of limited expected value). Integrating x^2 gets you x^3 with various denominators.

Anything from Course 3 is fair game for the Course 4 exam, as people who took the last sitting will tell you.

Bama Gambler
07-15-2003, 10:19 AM
AVI, check out the bumped thread ASM v5 #4.4

Avi
07-16-2003, 09:16 AM
Thank you, both.

I now understand what confused me.

Off to MoM and MLE :crying: