Question

Insurance, Inc., a nonlife insurance company, insures customer properties, including jewelries. The company will insure a $50,000 diamond for its full value against theft at an annual premium of $400. Suppose that the probability that the diamond would be stolen is 0.005, and let xdenote the insurance company’s profit.

1. Set up the probability distribution of the random variable x.
2. Calculate the insurance company’s expected profit.
3. Find the premium that the insurance company should charge if it wants its expected profit to be $1,000.

Answer 1

Answer

(A) Probability distribution for the random variable x is

Profit(x)	P(x)
A	1-0.005 = 0.995
A-50000	0.005

A is the premium charge per policy

(B) Expected profit =

Στ* P(x)

= (A*0.995) + 0.005*(A-50000)

= 0.995A + 0.005A - 250

= (A - 250) dollars

(C) if it wants its expected profit to be $1,000, we have the following equation

$1000 = A - 250

or A = $1000+$250

A = $1250

Therefore, company should charge $1250 per policy