November 2001 - Course 1 SOA Solutions
November 2001 - Course 1 SOA Solutions
November 2001 - Course 1 SOA Solutions
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29. B<br />
Let X and Y denote repair cost and insurance payment, respectively, in the event the auto<br />
is damaged. Then<br />
⎧0 if x ≤ 250<br />
Y = ⎨<br />
⎩x<br />
− 250 if x > 250<br />
and<br />
2<br />
1500 1 1 2<br />
[ ] ( ) ( )<br />
1500 1250<br />
EY = ∫ x− 250 dx= x− 250<br />
250<br />
= = 521<br />
250<br />
1500 3000 3000<br />
3<br />
1500<br />
2 1 2 1 3 1500 1250<br />
E⎡ ⎣Y ⎤<br />
⎦ = ∫ ( x− 250) dx= ( x− 250)<br />
250<br />
= = 434,028<br />
250<br />
1500 4500 4500<br />
2<br />
2 2<br />
Var[ Y] = E⎡<br />
⎣Y ⎤<br />
⎦− { E[ Y]<br />
} = 434,028 −( 521)<br />
Var Y = 403<br />
[ ]<br />
<strong>Course</strong> 1 <strong>Solutions</strong> 18 <strong>November</strong> <strong>2001</strong>
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