UNSW
ACTL1001 Actuarial Studies and Commerce
Sample Solutions Exercises 8
Exercise 1
In this case
1. For the individual risks with random loss
L
E
[
L
] = 150
;
000
°
0
:
05
+ 75
;
000
°
0
:
05
+ 0
°
0
:
9
= 11
;
250
V ar
[
L
] = (150
;
000
±
11
;
250)
2
°
0
:
05
+ (75
;
000
±
11
;
250)
2
°
0
:
05
+ (0
±
11
;
250)
2
°
0
:
9
= 1
;
279
;
687
;
500
or a standard deviation of 35,772.7
2. See following table (note that there are faster ways of doing this by using
binomial). There are 27 possibilities for the combinations of possible
losses for the 3 risks.
The expected value is 11,250 (as is expected)
and the variance is 426,562,500 or a standard deviation of 20,653.4.
1

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