Actuarial Outpost SOA #93
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#1
05-08-2012, 04:56 AM
 jrmkr Member SOA Join Date: Apr 2012 Location: Sri Lanka Studying for FM College: University of Colombo. Senior year Posts: 43
SOA #93

In the solution, how X + Y = 8 became?

There was a graph so I unable to post it here.

The question is:

A family buys two policies from the same insurance company. Losses under the two policies are independent and have continuous uniform distributions on the interval from 0 to 10. One policy has a deductible of 1 and the other has a deductible of 2. The family experiences exactly one loss under each policy.

Calculate the probability that the total benefit paid to the family does not exceed 5.
#2
05-08-2012, 07:21 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,464

The deductibles. If, for example, X=1 and Y=7, the payment is (X-1)+(Y-2)=5.

Note that if X<1 or Y<2, X+Y=8 is not the boundary.
#3
05-08-2012, 09:01 AM
 jrmkr Member SOA Join Date: Apr 2012 Location: Sri Lanka Studying for FM College: University of Colombo. Senior year Posts: 43

Quote:
 (X-1)+(Y-2)=5.
Nice trick. Thanks.

Quote:
 If X<1 or Y<2, X+Y=8 is not the boundary.
It is true. But when integrating it is(the boundary) the limit as same as when X=1 and Y=2. Please could you explain it?
#4
05-08-2012, 09:51 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,464

It is OK when X>=1 and Y>=2. It is only a problem if X<1 or Y<2, because if X<1 the benefit for X is 0, not X-1; similarly for Y.

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