Sponsored Ads
Pauline Reimer, ASA, MAAA
Pryor Associates
Actuarial Openings: Life, P&C, Health, Pensions, Finance
Ezra Penland Actuarial Recruiters
Top Actuary Jobs
Salary Surveys Apply Bios Casualty Health Life Pension

Results 1 to 2 of 2

Thread: Finan 31.16 (but really need help with all convolution)

  1. #1
    Actuary.com - Newbie Poster
    Join Date
    Dec 2013
    Posts
    1

    Finan 31.16 (but really need help with all convolution)

    Hello all,

    I am currently working on studying exam and had some questions regarding using convolution for the continuous case of the sum of two independent random variables. I have no problem with the actual integration, but what is troubling me is finding the bounds.


    31.16 Consider two independent random variables X and Y. Let fx(x) = 1 - (x/2) for 0<=x<=2 and 0 otherwise. Let fy(y) = 2-2y for 0<=y<=1 and 0 otherwise. Find the probability density function of X+Y.



    -for a = x+y

    (fx*fy)(a) (the convolution) is the integral from negative infinity to infinity of fx(a-y)fy(y)dy or fy(a-x)fxdx


    For 0<=a<=1 I integrate using the above formula and get

    2a-(3/2)a^2 + (1/6)a^3

    I would have thought the bounds to be from 0 to 1 but they are actually from 0 to a. And for the other cases of a (where 1<=a<=2 and 2<=a<=3) I am having trouble finding out where the bounds are. I am having trouble with basically all of these problems (discrete case as well) on finding the bounds and I really can't move forward until I fully understand so some insight would greatly be appreciated! Thanks!

  2. #2
    Actuary.com - Posting Master
    Join Date
    Oct 2007
    Posts
    3,110
    Reading this thread may help: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=257082&highlight=convolution

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Similar Threads

  1. Convolution problem please help ?
    By wahibr in forum Actuarial - Ask the Professor
    Replies: 0
    Last Post: May 13th 2010, 11:33 PM
  2. convolution S=x1 + x2 + x3
    By rahim in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 1
    Last Post: April 15th 2010, 10:56 PM
  3. Convolution Method
    By jamesy628 in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 2
    Last Post: June 11th 2008, 12:11 PM
  4. convolution?
    By Fermat83 in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 3
    Last Post: October 23rd 2007, 03:20 AM

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •