Actuarial Outpost May 00 #18 .
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

#1
04-05-2006, 02:51 PM
 Crazycow Member Join Date: Aug 2005 Posts: 76
May 00 #18 .

Can any1 help me wif this? The question looks real simple. Tried to do it using 1st & 2nd moment , but consistently get bad answer.

Esitmate A: E(uA)= 1000 sd(uA)= 400
Estimate B: E(uB)= 1200 sd(uB)= 200

Estimate C is a weighted avg of the 2 esitmates A & B

uC = w. uA +(1-w).uB

Determine the value of w that minimise sd (uC).

I mean I understand the solution but I dont understand why using 1 & 2 moments dont work.
__________________
Every SoA paper is like giving birth. Every June & December is like confinement month....

Good luck to all.....pwn the paper!!!

Last edited by Crazycow; 04-05-2006 at 04:08 PM..
#2
04-05-2006, 03:52 PM
 Surfohio Member Join Date: Apr 2005 Posts: 1,645

It works for me to use 1st and 2nd moments, but I end up with the same equation as in the solution, Var(C) = w^2 Var(A) + (1-w)^2 Var(B)
#3
04-05-2006, 04:06 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 6,198

Perhaps you misunderstood the problem and calculated it as a mixture? This is a weighted sum of random variables, so the second moment is
$E[(w\mu_A+(1-w)\mu_B)^2]=w^2E[\mu_A^2]+2(w)(1-w)E[\mu_A\mu_B]+(1-w)^2E[\mu_B^2]$
You'd then use independence to factor the second summand, and use the facts given. This is the hard way to do the problem, though.
#4
04-05-2006, 04:18 PM
 Crazycow Member Join Date: Aug 2005 Posts: 76

I did read it as a mixture distribution. Thx
__________________
Every SoA paper is like giving birth. Every June & December is like confinement month....

Good luck to all.....pwn the paper!!!
#5
04-06-2006, 09:17 AM
 Wendy Crewson Member SOA AAA Join Date: Jun 2005 Location: Holding on with white knuckles Favorite beer: Mickey's Big Mouth Posts: 346
Weighted sum vs. mixture

I get confused about how to tell the difference between a weighted sum of random variables and a mixture. There is an example in Mahler's notes in the simulation section where he tries to make the distinction, but it is not clear to me. Is it just a matter of being told whether we are dealing with a weighted sum versus a mixture?? Any thoughts would be appreciated. Keep in touch.
__________________
Liz Lemon's Mom on why she didn't pursue marriage to Buzz Aldrin: "It wasn't that simple, Liz. I had just graduated from secretarial school, and I got a job at Sterling Cooper."
#6
04-06-2006, 11:44 AM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 6,198

If random variables are added, that's a sum (weights don't have to add up to 1). If distribution functions (F) or density functions (f) are added together (with weights adding up to 1), that's a mixture.
#7
04-06-2006, 02:11 PM
 Crazycow Member Join Date: Aug 2005 Posts: 76

Dr Abe, u r leet.
__________________
Every SoA paper is like giving birth. Every June & December is like confinement month....

Good luck to all.....pwn the paper!!!

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 09:50 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top