Question

An insurance company will insure a $50,000 diamond for its full value against theft at a premium of $400 year. Suppose that the probability that the diamond will be stolen is .05, and let x denote the insurance company's profit.

1. Set up the probability 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 $1000.00.

Answer 1

Here let us given that , if diamond wasn't theft then profit in the year = $400

If diamond was theft then the loss = $50000 - $400

= $49600

a)To determine the probability of the random variable x

i.e.,

P(X = 400) = 0.995

P(X = - 49600) = 0.005

b)

To give the expected profit

Consider,

E[x] = - 49600 * 0.005 + 400*0.995

= -248 + 398

E[x] = $ 150

Thus the insurance company's expected profit = $ 150

c)

To give the premium that the insurance company should charge if it wants its expected profit to be $1000.00

Let us assume that the new premium be x

So the new expected profit = (x - 50000) * 0.005 + x*0.995 = $1000

- 250 + 0.005x + 0.995x = 1000

x = 1000+250

x = $1250