Actuarial Discussion Forum - Professional Discussions for Professional Actuaries

Actuarial Jobs from Actuary.com    Submit Your Actuarial Resume Anonymously
Other Insurance Jobs    Other Financial Jobs    Other Health Jobs    Other IT Jobs    Other Jobs, Careers and Employment    Actuarial News
Directory of Actuarial Exam Study Courses - Online    Directory of Actuarial Exam Study Materials    Directory of Actuarial Exam Study Seminars - Live
Directory of Actuarial Recruiters    Directory of Actuarial Schools    Actuarial Grads Network    Actuary.com 



D.W. Simpson & Co, Inc. - Worldwide Actuarial Jobs
Life Jobs 
Health Jobs Pension Jobs Casualty Jobs Salary Apply
Pauline Reimer, ASA, MAAA - Pryor Associates
Nat'l/Int'l Actuarial Openings: Life P&C Health Pensions Finance
ACTEX Publications and MadRiver Books
Serving students worldwide for over 40 years
Advertise Here - Reach Actuarial Professionals
Advertising Information
Actuarial Careers, Inc. - Actuarial Jobs Worldwide
Search positions by geographic region, specialization, or salary
Ezra Penland Actuarial Recruiters - Top Actuarial Jobs
Salary Surveys  Apply Online   Bios   Casualty   Health   Life   Pension

+ Reply to Thread
Results 1 to 10 of 10

Thread: Dr. Ostaszewski Practice Problem # 12 on exam 19

  1. #1
    Actuary.com - Level II Poster
    Join Date
    Feb 2011
    Location
    NY
    Posts
    60

    Dr. Ostaszewski Practice Problem # 12 on exam 19

    A dart is thrown at a board with radius 7. the point the dart hits is uniformly distributed on the cricular board. Find the expected distance of the point from center of board. The answer uses the survival function but I do not how exactly. I am not a mathematician and need help. I just like math thats all. It says s(t)= T>t= Pr (X^2 +Y^2 > t^2) = area of circle with r=7-area pfcircle with r=t/ area of circle with r=7. I am lost ......

  2. #2
    Actuary.com - Level II Poster
    Join Date
    Feb 2011
    Location
    NY
    Posts
    60
    I understand that the integral of the survival gives the expected value thats all though.

  3. #3
    Actuary.com - Level II Poster
    Join Date
    Feb 2011
    Location
    NY
    Posts
    60
    Can anyone explain what this survival function means in English?

  4. #4
    Actuary.com - Level III Poster
    Join Date
    Nov 2009
    Location
    New York
    Posts
    214
    Hello Pete! Fellow New Yorker here as well

    You may find a definition of the Survival Function here

    [url]http://en.wikipedia.org/wiki/Survival_function[/url]

    are you using a manual to prepare for P? I highly recommend you do so! Googling is just not enough sometimes :P

    To put the definition in english though... I would say it's easy to think of the survival function S[X] is the equivalent of saying the probability that something survives for X length of time, which is to say that it "dies" after X length of time. So you may think of it as P[X>x] which is the converse of F[x] which says something "dies" before x or P[X<x]

    The relationship between S[X], F[X], and f[X] is something that you definitely need to be aware of for this exam. Hope that helped!!

  5. #5
    Actuary.com - Level II Poster
    Join Date
    Feb 2011
    Location
    NY
    Posts
    60
    Thank you Sir.... I am not sure what your name is but I appreciate the info. I just do not get what the equation means in this problem like how does T >t = that equation with the areas. I failed P 3 times with my highest score at 5. I practice a little here and there thinking I might learn a little a more. I am now using Dr. Ostaszewski's manual.

  6. #6
    Actuary.com - Level II Poster
    Join Date
    Feb 2011
    Location
    NY
    Posts
    60
    No answers? How does the distance formula fit with the T in the survival?

  7. #7
    Actuary.com - Level III Poster
    Join Date
    Nov 2009
    Location
    New York
    Posts
    214
    Quote Originally Posted by pete2323 View Post
    No answers? How does the distance formula fit with the T in the survival?
    Well.... you can consider the length from the origin a joint pdf yes? You can expect a Y and expect an X. And depending on those X and Y you'll calculate your expected distance from the origin. (pythagorus here!)

    But I think the easy solution here would be to recognize this is a uniform distribution... What can you draw from that? You can come up with you p(x) your F(x) and your S(x).

    It's easy to calculate E[x] from any of those bits of information. In this problem they utilized S[x] and the identity that Integral from 0 to Inf of S[x] equal E[x]. But since this is a uniform distribution it cuts out all the calculus. Your S[x] is just area of hitting the board between x and 7 out of the area of the whole board. (we are using areas because it is a uniform distribution and it's easier than integrating joint distribution here) To put it in steps I would say this.....

    Need E[x]

    Acquire S[x]

    Integrate

    You should get 4 and 2/3. Is this correct?

    I feel like this is still confusing so I'm hoping someone else can come in and save the day :lol:

  8. #8
    Actuary.com - Level II Poster
    Join Date
    Feb 2011
    Location
    NY
    Posts
    60

    Dart Problem

    Thanks again.... I think I get it now....... You can figure out what F(X) is, just the (area of circle with r=x)/(area of circle with r=7), then 1-F(x) would = S (X), then you could finally integrate that function from 0 to 7 to get the answer. Thanks...... I think thats right? What your name, maybe we can study sometime if your from NY.

  9. #9
    Actuary.com - Level III Poster
    Join Date
    Nov 2009
    Location
    New York
    Posts
    214
    anytime dude double check that answer though! It's been a lil while since I looked at p :P

    I passed p and fm last year and was hoping to sit for MLC this may but decided to move it back to Nov (ugh...)

    But yeah man I'm totally down to network especially with other New Yorkers! I'll PM you my facebook. I've got some notes somewhere if you are interested. What manual are you using???

    Oh and my name is Renny Nice to meet ya!

  10. #10
    Actuary.com - Level II Poster
    Join Date
    Feb 2011
    Location
    NY
    Posts
    60
    14/3 is the answer

+ Reply to Thread

Thread Information

Users Browsing this Thread

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

     

Similar Threads

  1. Weekly Practice Exam "FM" Problems courtesy of Dr Krzysztof Ostaszewski
    By krzysio in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 442
    Last Post: April 11th 2013, 01:49 PM
  2. Weekly Practice Exam "P" Problems courtesy of Dr Krzysztof Ostaszewski
    By admin in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 699
    Last Post: April 11th 2013, 01:45 PM
  3. Weekly Exam MLC Practice Exercises & Problems courtesy of Krzys' Ostaszewski
    By admin in forum SOA Exam MLC - Actuarial Models, Life Contingencies - with practice exam problems
    Replies: 259
    Last Post: October 8th 2010, 04:48 PM
  4. are you doing practice exam 19 by Dr. Krzysztof Ostaszewski?
    By saccharineSarah in forum SOA Exam P / CAS Exam 1 - Probability - with practice exam problems
    Replies: 0
    Last Post: June 12th 2010, 11:03 PM
  5. ASM Practice Exam #5 Problem 4
    By mjlee08 in forum SOA Exam FM / CAS Exam 2 - Financial Mathematics - with practice exam problems
    Replies: 3
    Last Post: May 26th 2008, 10:27 PM

Bookmarks - Share

Bookmarks - Share

Posting Permissions

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