Question

Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution below describes expected property losses for the group of 6 buildings. Assume that the property exposures are independent of each other.

Losses $                                                          Probability of Loss

$10,000                                                           0.20

$20,000                                                           0.10

$50,000                                                           0.06

$100,000                                                         0.03

$500,000                                                         0.01

1. Find the average or expected loss of the group of buildings in a given year.

2. Calculate the standard deviation of the distribution.

3. Find the Coefficient of Variation.

4. What is Terry’s actuarially fair premium?

Answer 1

(a) mean/average loss=expected loss=E(x)=sum(x*p(x))=15000

(b) standard deviation(sd)=sqrt(variance)=sqrt(2785000000)=52773 ( whole number approximation)

variance=E(x²)-E(x)*E(x)=3010000000-15000*15000=2785000000
E(x²)=sum(x²*p(x))=3010000000

(c) coefficient of variation=sd/mean=100*52773/15000=351.82%

(d) Terry’s actuarially fair premium would be expected loss=15000

x	p(x)	x*p(x)	x2*p(x)
10000	0.2	2000	20000000
20000	0.1	2000	40000000
50000	0.06	3000	150000000
100000	0.03	3000	300000000
500000	0.01	5000	2500000000
	sum=	15000	3010000000