Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Short-Term Actuarial Math
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

Search Actuarial Jobs by State @ DWSimpson.com:
AL AK AR AZ CA CO CT DE FL GA HI ID IL IN IA KS KY LA
ME MD MA MI MN MS MO MT NE NH NJ NM NY NV NC ND
OH OK OR PA RI SC SD TN TX UT VT VA WA WV WI WY

Short-Term Actuarial Math Old Exam C Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 06-14-2017, 10:06 PM
degenerateFunction degenerateFunction is offline
SOA
 
Join Date: May 2017
College: UCLA
Posts: 9
Default question on limited expected value

Say you want to find E [ X + 50 ^ 1000 ]

Is this equivalent to E [ X ^ 950 ] ?
Reply With Quote
  #2  
Old 06-14-2017, 10:22 PM
Gandalf's Avatar
Gandalf Gandalf is offline
Site Supporter
Site Supporter
SOA
 
Join Date: Nov 2001
Location: Middle Earth
Posts: 31,286
Default

No. It is a strange thing you are asking about, but I don't think your conclusion is right.

First, I think you must mean E[(X+50)^1000]. Parentheses may not matter, but I assume this is what it meant. Then, suppose (as a counterexample showing the equality is not valid) X is always 2000. X+50 is always 2050, so E[(X+50)^1000] = 1000. But E(X^950) is 950.
Reply With Quote
  #3  
Old 06-14-2017, 10:30 PM
Vorian Atreides's Avatar
Vorian Atreides Vorian Atreides is online now
Wiki/Note Contributor
CAS
 
Join Date: Apr 2005
Location: As far as 3 cups of sugar will take you
Studying for ACAS
College: Hard Knocks
Favorite beer: Most German dark lagers
Posts: 65,723
Default

In general, no.

Consider the formula for E[ X ^ d ] where S(y) = 1 - F(y):


Then:


Do some algebra, then work out the formula for E[ X ^ (d - k)], and you'll find that
__________________
I find your lack of faith disturbing

Why should I worry about dying? Itís not going to happen in my lifetime!


Freedom of speech is not a license to discourtesy

#BLACKMATTERLIVES

Last edited by Vorian Atreides; 06-14-2017 at 10:58 PM.. Reason: adding clarifying ()'s
Reply With Quote
  #4  
Old 06-14-2017, 10:56 PM
degenerateFunction degenerateFunction is offline
SOA
 
Join Date: May 2017
College: UCLA
Posts: 9
Default

Thank you both. And yes, I meant it as you wrote it, Gandalf.
Reply With Quote
Reply

Tags
soa

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

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 04:49 PM.


Powered by vBulletin®
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.13054 seconds with 11 queries