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Thread: Soa #36

  1. #1
    Actuary.com - Level I Poster
    Join Date
    Aug 2013
    Posts
    23

    Soa #36

    Please break the solution into more steps to help me understand.

    A group insurance policy covers the medical claims of the employees of a small
    company. The value, V, of the claims made in one year is described by
    V = 100,000Y
    where Y is a random variable with density function
    (1 )4 for 0 1
    ( )
    0 otherwise,
    k y y
    f y
    ⎧ − < <
    =⎨⎩
    where k is a constant.
    What is the conditional probability that V exceeds 40,000, given that V exceeds 10,000?
    (A) 0.08
    (B) 0.13
    (C) 0.17
    (D) 0.20
    (E) 0.51

    Solution to be broken down further:

    Solution:B
    Todeterminek,notethat
    1=    
    1
    4 51
    0
    0
    1 1
    5 5
    ! k  y dy   k  y  k 
    k=5
    WenextneedtofindP[V>10,000]=P[100,000Y>10,000]=P[Y>0.1]
    =    
    1
    4 51
    0.1
    0.1
    ! 5 1 y dy   1 y =(0.9)5=0.59andP[V>40,000]
    =P[100,000Y>40,000]=P[Y>0.4]=    
    1
    4 51
    0.4
    0.4
    ! 5 1 y dy   1 y =(0.6)5=0.078.
    ItnowfollowsthatP[V>40,000V>10,000]
    = [ 40,000 10,000] [ 40,000] 0.078
    [ 10,000] [ 10,000] 0.590
    P V V P V
    P V P V
    # # #
     
    # #
    =0.132.

    Here are the urls to the sample questions below:
    http://www.soa.org/Files/Edu/edu-exam-p-sample-quest.pdf
    http://www.soa.org/Files/Edu/edu-exam-p-sample-sol.pdf

  2. #2
    Actuary.com - Posting Master
    Join Date
    Oct 2007
    Posts
    3,110
    Copy/pasting is a bad idea... what's your question?

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