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ASSIGNMENT 3 – ACTSC 431/831, FALL 2008
Due at the beginning of the class on Tuesday, October 21
.
1. Let loss
X
have a threecomponent spliced distribution. The pdf of
X
has the following form:
f
X
(
x
) =
0
,
x <
0
,
0
.
06
,
0
≤
x <
5
,
0
.
1
,
5
≤
x <
10
,
a
x
4
,
x
≥
10
.
(a) Calculate the variance of the loss.
[6 marks]
(b) Calculate the distribution function
F
X
(
x
) of the loss for all
x
∈
(
∞
,
∞
).
[6 marks]
(c) Calculate the probability that the loss is between 4 and 8.
[2 marks]
2. Let
N
be the number of claims in an insurance portfolio. The sizes of claims in the portfolio
are i.i.d. random variables with common
Pareto
(3
,
50) distribution. Furthermore, the sizes of
claims are independent of
N
. Let
N
1
be the number of claims of sizes between 5 and 10 and
N
2
be the number of claims of sizes larger than their expectation.
(a) Assume that
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 Fall '09
 david

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