Question

An insurance company will insure a $50,000 diamond for its full value against theft at a premium of $400 per year. Suppose that the probability that the diamond will be stolen is .005, and let x denote the insurance company's profit. a) Set up the probability distribution of the random variable x. b) Calculate the insurance company's expected profit. c) Find the premium that the insurance company should charge if it wants its expected profit to be $1,000.

Answer 1

If diamond does not gets stolen profit in the year = $400

If diamond gets stolen the loss = $50000 - $400 = $49600

Therefore the probability distribution of the random variable x =

a)

P(X = 400) = 0.995

P(X = -49600) = 0.005

b)

E[x] = -49600 * 0.005 + 400*0.995 = $150

Hence insurance company's expected profit = $150

c)

Let the new premium be x

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

solving the above equation we get x = $1250