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1. ## 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
Todeterminek,notethat
1=    
1
4 51
0
0
1 1
5 5
! k  y dy   k  y  k 
k=5
WenextneedtofindP[V>10,000]=P[100,000Y>10,000]=P[Y>0.1]
=    
1
4 51
0.1
0.1
! 5 1 y dy   1 y =(0.9)5=0.59andP[V>40,000]
=P[100,000Y>40,000]=P[Y>0.4]=    
1
4 51
0.4
0.4
! 5 1 y dy   1 y =(0.6)5=0.078.
ItnowfollowsthatP[V>40,000V>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

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